In recent decades, considerable progress has been made in our understanding of emotional development. Yet no single current theory can fully encompass all of the empirical findings. Herein I propose that aspects of several theoretical approaches can be incorporated into a novel view that is informed by the dynamical systems perspective.

We show how a simple nonlinear dynamical system (the discrete quadratic iteration on the unit segment) can be the basis for modelling the embryogenesis process. Such an approach, even though being crude, can nevertheless prove to be useful when looking with the two main involved processes:i) on one hand the cell proliferation under successive divisions ii) on the other hand, the differentiation between cell lineages. We illustrate this new approach in the case of Caenorhabditis elegans by looking at the (...) early stages of embryogenesis, up to several hundreds of cells (lima bean larval stage). We show how the many results that have been obtained by several groups can be interpreted in terms of values for the parameters controlling the dynamical system. Furthermore, we can extend the model to the cases of genetic mutations. More precisely the teratogenetic and lethal effects are associated with abnormal variation of the control parameters with time. (shrink)

Perfect adaptation in a dynamical system is the phenomenon that one or more variables have an initial transient response to a persistent change in an external stimulus but revert to their original value as the system converges to equilibrium. With the help of the causal ordering algorithm, one can construct graphical representations of dynamical systems that represent the causal relations between the variables and the conditional independences in the equilibrium distribution. We apply these tools to formulate sufficient (...) graphical conditions for identifying perfect adaptation from a set of first-order differential equations. Furthermore, we give sufficient conditions to test for the presence of perfect adaptation in experimental equilibrium data. We apply this method to a simple model for a protein signalling pathway and test its predictions in both simulations and using real-world protein expression data. We demonstrate that perfect adaptation can lead to misleading orientation of edges in the output of causal discovery algorithms. (shrink)

In philosophical studies regarding mathematical models of dynamical systems, instability due to sensitive dependence on initial conditions, on the one side, and instability due to sensitive dependence on model structure, on the other, have by now been extensively discussed. Yet there is a third kind of instability, which by contrast has thus far been rather overlooked, that is also a challenge for model predictions about dynamical systems. This is the numerical instability due to the employment of (...) numerical methods involving a discretization process, where discretization is required to solve the differential equations of dynamical systems on a computer. We argue that the criteria for numerical stability, as usually provided by numerical analysis textbooks, are insufficient, and, after mentioning the promising development of backward analysis, we discuss to what extent, in practice, numerical instability can be controlled or avoided. (shrink)

Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations' solutions, such as orbital resonances and horseshoe orbits. (...) Poincaré wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating. (shrink)

This paper proposes a novel robust fixed-time control for the robot manipulator system with uncertainties. Based on the uniform robust exact differentiator algorithm, a robust control term is constructed. Then, a robust fixed-time inverse dynamics control is proposed. For the proposed control method, the fixed-time stability of a closed-loop system with uncertainties is strictly proved. The newly proposed method exhibits the following two attractive features. First, the proposed control scheme extends the existing fixed-time IDC for the robot manipulator system to (...) the robust control scheme. Second, the proposed method is strictly nonsingular rather than the commonly used approximate approach. Simulation result demonstrates the effectiveness of the proposed control scheme. (shrink)

This paper proposes a Cournot game organized by three competing firms adopting bounded rationality. According to the marginal profit in the past time step, each firm tries to update its production using local knowledge. In this game, a firm’s preference is represented by a utility function that is derived from a constant elasticity of substitution production function. The game is modeled by a 3-dimensional discrete dynamical system. The equilibria of the system are numerically studied to detect their complex characteristics (...) due to difficulty to get an explicit form for those equilibria. For the proposed utility function, some cases with different value parameters are considered. Numerical simulations are used to provide an experimental evidence for the complex behavior of the evolution of the system. The obtained results show that the system loses its stability due to different types of bifurcations. (shrink)

Mechanistic explanations are often said to explain because they reveal the causal structure of the world. Conversely, dynamical models supposedly lack explanatory power because they do not describe causal structure. The only way for dynamical models to produce causal explanations is via the 3M criterion: the model must be mapped onto a mechanism. This framing of the situation has become the received view around the viability of dynamical explanation. In this paper, I argue against this position and (...) show that dynamical models can themselves reveal causal structure and consequently produce nonmechanistic, dynamical explanations. Taking the example of cell fates from systems biology, I show how dynamical models, and specifically the attractor landscapes they describe, identify the causes of cell differentiation and explain why cells select particular fates. These dynamical features of the system better fit Woodward’s (2010, 2018) criteria of specificity and proportionality and make them the best candidate causes of cell fates than mechanisms. I also show how these causes are irreducible and inaccessible to mechanistic models, making 3M unworkable and counterproductive in this case. Dynamical models can reveal dynamical causes and thereby provide causal explanations. (shrink)

In this paper, we propose a new predator-prey nonlinear dynamic evolutionary model of real estate enterprises considering the large, medium, and small real estate enterprises for three different prey teams. A 5D predator-prey nonlinear dynamic evolutionary system in the real estate market is established, where the large, medium, and small real estate enterprises correspond to three differential equations, provincial and local officials, and the central government correspond to the other two differential equations. Nonlinear dynamic analysis on a 5D predator-prey evolutionary (...) system in the real estate market, containing the analysis of equilibrium points and stabilities, is made. The corresponding discrete system is simulated, and the simulation results about Lyapunov spectrum, bifurcation diagram, sequence diagram, and phase diagram are given. Compared with the work of Yang et al. in which all real estate enterprises corresponded to one differential equation, in our proposed model, the large, medium, and small real estate enterprises correspond to three differential equations which is more accordant with the specific circumstance of real estate companies. (shrink)

Is the brain really a computer? In particular, is our intelligence a computational achievement: is it because our brains are computers that we get on in the world as well as we do? In this paper I will evaluate an ambitious new argument to the contrary, developed in Landgrebe and Smith (2021a, 2022). Landgrebe and Smith begin with the fact that many dynamical systems in the world are difficult or impossible to model accurately (inter alia, because it is (...) intractable to find exact solutions to the differential equations that describe them—meaning we have to approximate—but at the same time they are such that small differences in starting conditions lead to big differences in final conditions, thwarting accurate approximation). Yet we manage to survive and thrive in a world full of such systems. Landgrebe and Smith argue from these premises that it is not because our brains are computers that we get on as well as we do: instead it is because of the various ways that we dynamically couple with such systems, these couplings themselves impossible to model well enough to emulate in silico. Landgrebe and Smith thus defend a dynamical systems model in the lineage of Gibson (1979), Van Gelder (1995), and Thompson (2007), though their focus is on decisively refuting the computationalist alternatives rather than developing the positive account. Here I will defend the claim that human intelligence is genuinely computational (and that whole brain emulation and others forms of AGI may be possible) against this argument. (shrink)

This paper deals with stochastically globally exponential stability for stochastic impulsive differential systems with discrete delays and infinite distributed delays. By using vector Lyapunov function and average dwell-time condition, we investigate the unstable impulsive dynamics and stable impulsive dynamics of the suggested system, and some novel stability criteria are obtained for SIDSs with DDs and IDDs. Moreover, our results allow the discrete delay term to be coupled with the nondelay term, and the infinite distributed delay term to be coupled (...) with the nondelay term. Finally, two examples are given to verify the effectiveness of our theories. (shrink)

Every physical theory has two different forms of mathematical equations to represent its target systems: the dynamical and the kinematical. Kinematical constraints are differentiated from equations of motion by the fact that their particular form is fixed once and for all, irrespective of the interactions the system enters into. By contrast, the particular form of a system's equations of motion depends essentially on the particular interaction the system enters into. All contemporary accounts of the structure and semantics of (...) physical theory treat dynamics, i.e., the equations of motion, as the most important feature of a theory for the purposes of its philosophical analysis. I argue to the contrary that it is the kinematical constraints that determine the structure and empirical content of a physical theory in the most important ways: they function as necessary preconditions for the appropriate application of the theory; they differentiate types of physical systems; they are necessary for the equations of motion to be well posed or even just cogent; and they guide the experimentalist in the design of tools for measurement and observation. It is thus satisfaction of the kinematical constraints that renders meaning to those terms representing a system's physical quantities in the first place, even before one can ask whether or not the system satisfies the theory's equations of motion. (shrink)

A geometro-differential quantum theory of extended particles is presented. The geometrical selling is that of Hilbert fiber bundles whose base manifolds are pseudo-Riemannian space-times of points χ which are interpreted as partial aspects of physical reality (the extended particle). The fibers are carrier spaces of induced (internal configuration and momentum) representations of the structural group (the de Sitter group here). Sections of these bundles are seen as physical representations of the particle, and their values in the fibers are interpreted as (...) states of internally localized modes composing the particle. This geometrical structure is “analogous” to that of a geometro-stochastic quantization developed in recent years. The physical interpretation is a combination of those of an old functional quantum theory and of an induced representation scheme based on an interpretation of intertwining, between configuration and momentum representations, as localization, materialization, and propagation of particles. Our model is applied in two cases: (1) Induced representation is applied in both space-time and internal space: both have de Sitter symmetry whose connection is ignored. Intertwining is considered in both spaces in a composed fashion. (2) For generic spacetimes and when the connection is taken into account, intertwining is applied only in the internal space. Parallel transport is combined with intertwining for a redefinition of localization, materialization, and propagation (the latter in a path integral context inspired from geometro-stochastic quantization). (shrink)

Recent advances in the theory of dynamical systems, set-valued analysis, and viability theory offer new and interesting perspectives on the shaping of social and historical time. Specific aspects of these theories are presented in several different areas to show their concrete applications in history and historical demo-economy, and a parallel is established with novelist Tanizaki's fictional technique. In connection with this, McCloskey's 1991 comparison of storytelling with deterministic chaos is discussed and a critique of other models concerned with (...) unpredictability in human affairs provided. Finally, the shapings of social and historical time are described in terms of the viable strategies at the heart of evolutionary processes involving human agents interacting with a variety of constraints. (shrink)

Recognition of the plasticity of development — from gene expression to neuroplasticity — is increasingly undermining the traditional distinction between structure and function, or anatomy and behavior. At the same time, dynamic systems theory — a set of tools and concepts drawn from the physical sciences — has emerged as a way of describing what Maurice Merleau-Ponty calls the “dynamic anatomy” of the living organism. This article surveys and synthesizes dynamic systems models of development from biology, neuroscience, and (...) psychology in order to propose an integrated account of growth, learning, and behavior. Key to this account is the concept of self-differentiation or symmetry-breaking. I argue that development can be understood as a cascade of symmetry-breaking events brought about by the ongoing interactions of multiple, nested, nonlinear dynamic systems whose self-organizing behaviors gradually alter their own anatomical conditions. I begin by introducing the concept of symmetry-breaking as a way of understanding anatomical development. I then extend this approach to motor development by arguing that the organism’s behavior grows along with its body, like a new organ. Finally, I argue that the organism’s behavior and its world grow together dialectically, each driving the other to become more complex and asymmetrical through its own increasing asymmetry. Thus development turns out to be a form of cognition or sense-making, and cognition a form of development. (shrink)

The aim of this work is to present aggregation methods of hierarchically organized systems allowing one to replace the initial micro-system by a macro-system described by a few global variables. We also study the relations between the fast micro-dynamics and the slow macro-dynamics which can produce global properties. Emergence corresponds to a bottom-up coupling that is the result effected by a micro-level at a macro-level. As an example, we present prey-predator models with different time scales in an heterogeneous environment. (...) A fast time scale is associated to the migration process on spatial patches and a slow time scale is associated to growth and interactions between the populations. Preys must go on spatial patches where resources are located and where predators can attack them. The efficiency of the predators to catch preys is patch dependent. Perturbation methods allow us to aggregate the initial system of differential equations for the patch sub-populations into a macro-system of two differential equations governing the total population densities. We study the case of density independent and density dependent migrations. In the latter case, we show that different functional responses can emerge in the macro prey-predator model as a result of the coupling between the slow and fast systems. (shrink)

Even the simplest cell exhibits a high degree of functional differentiation (FD) realized through several mechanisms and devices contributing differently to its maintenance. Searching for the origin of FD, we briefly argue that the emergence of the respective organizational complexity cannot be the result of either natural selection (NS) or solely of the dynamics of simple self-maintaining (SM) systems. Accordingly, a highly gradual and cumulative process should have been necessary for the transition from either simple self-assembled or self-maintaining (...) class='Hi'>systems of functionless structural components to systems with FD. We follow results of recent in vitro experiments with respect to competition among protocells, where a primitive type of selection begins to operate among them accompanied by a parallel evolution of their functional domain. We argue that minimal forms of FD should be established within the evolution of SM processes in protocells as they undergo a simpler selection process for stability and persistence in a prebiotic environment. We then suggest the concept of closure of constraints (CoC) as a way to identify and describe minimal FD in a far-from-equilibrium SM organization. We show in detail how the concept of CoC together with the conditions for its fulfillment can be applied in the case of a simple protocellular system that begins to couple internal chemical reactions with the formation of its membrane components. Finally, we discuss how such SM systems can evolve towards significantly higher levels of FD, suggesting this is mainly the result of functional recombination (formation of mechanisms) in the context of a modular SM organization. (shrink)

Dynamical-systems analysis is nowadays ubiquitous. From engineering (its point of origin and natural home) to physiology, and from psychology to ecology, it enjoys surprisingly wide application. Sometimes the analysis rings decisively false—as, for example, when adopted in certain treatments of historical narrative; other times it is provocative and controversial, as when applied to the phenomena of mind and cognition. Dynamical systems analysis (or “Systems” with a capital “S,” as I shall sometimes refer to it) is (...) simply a tool of analysis. It mobilizes the language and mathematical technology of differential equations, and brings into play the distinctive concepts of equilibrium and attractor, as well as gain, coupling and neighborhood, that are not obviously proprietary property of any particular domain of objects or regime in the world. It is the ecumenical language of engineers, universal in scope. Still, Systems, as a mode of analysis, itself stands in need of clarification. Once that clarity has been attained, one can then ask: are there limitations or bounds on proper application of Systems analysis, that are themselves premised upon considerations internal to the analysis itself? This is one of several questions to which the present essay is devoted. Before it can be attempted, however, we shall require some groundwork that clarifies the mode of analysis that is Systems—the family of analyses to which it belongs. This will begin to bring out (among other things) the precise difference of subject matter between biology and physics. And the ecumenicality of Systems analysis is bound to have its own distinctive commitments, as we shall see. Practitioners attuned to the signal characteristics of Systems analysis—characteristics that set it apart—proclaim its many advantages. (shrink)

Morphogenesis is a key process in developmental biology. An important issue is the understanding of the generation of shape and cellular organisation in tissues. Despite of their great diversity, morphogenetic processes share common features. This work is an attempt to describe this diversity using the same formalism based on a cellular description. Tissue is seen as a multi-cellular system whose behaviour is the result of all constitutive cells dynamics. Morphogenesis is then considered as a spatiotemporal organization of cells activities. We (...) show how this formalism relies on Reaction–Diffusion/Positional Information approach and how it permits to generalize its modelling possibilities. Three quite different applications for concrete morphogenetic processes are presented. The first one is a model for epithelial invagination, the second is a model of cellular differentiation by local cell–cell signalling. The last example is the secondary radial growth of conifer trees. From the mathematical point of view, different modelling tools are used according to the specificity of each process. (shrink)

It has been reported in non-contingent schedules that the variety of patterns of behavior is affected by the temporal variation of water deliveries. While temporal variation is accomplished by delivering water at fixed or variable times, spatial variation is usually accomplished by varying the number of dispensers and distance among them. Such criteria do not consider the possible ecological relevance of the location of water dispensers. Nevertheless, it is plausible to suppose that the intersection of the programed contingencies, the ecological (...) differentiated space, and the relative location of relevant objects and events could set up an integrated system with the behavioral patterns of the organism. In the present study, we evaluated the eco-functional relevance of two locations of the dispensers upon behavioral dynamics in Wistar rats using fixed and variable time schedules in a modified open-field system. In Experiment 1, three subjects were exposed to a fixed time 30-s water delivery schedule. In the first condition, the water dispenser was located at the center of the experimental chamber. In the second condition, the water dispenser was located at the center of a wall of the experimental chamber. Each location was present for 20 sessions. In Experiment 2, conditions were the same, but a variable time schedule was used. Routes, distance to the dispenser, recurrence patterns, time spent in zones, entropy, and divergence were analyzed. Our findings suggest a robust differential relevance of the location of the dispensers that should be considered in studies evaluating behavioral dynamics. Results are discussed from an integrative, ecological-parametric framework. (shrink)

James Clerk Maxwell’s 1865 paper, “A Dynamical Theory of the Electromagnetic Field,” is usually remembered as replacing the mechanical model that underpins his 1862 publication with abstract mathematics. Up to this point historians have considered Maxwell’s usage of Lagrangian dynamics as the sole important feature that guides Maxwell’s analysis of electromagnetic phenomena in his 1865 publication. This paper offers an account of the often ignored mechanical analogy that Maxwell used to guide him and his readers in the construction of (...) his new electromagnetic equations. The mechanical system consists of a weighted flywheel geared into two independently driven crank wheels in what amounts to a mechanical differential. I will demonstrate how Maxwell made use of the analogy between his flywheel system and electromagnetic induction to ground his study of electromagnetism in clear mechanical conceptions and to structure the derivation of the equations that together are now recognized as Maxwell’s equations for electrodynamics. By reconceiving specific components of his model in electromagnetic terms, while at the same time retaining many of the relations between concepts in the mechanical case, Maxwell gradually assembled increasingly generalized equations for electromotive force. Maxwell thus realized a much sought after balance between physical analogy and abstract mathematics in this, the last of his three seminal papers on electromagnetism. (shrink)

We investigate the dynamics of a nonautonomous stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis. By constructing suitable stochastic Lyapunov functions and using Has’minskii theory, we prove that there exists at least one nontrivial positive periodic solution of the system. Moreover, the sufficient conditions for extinction of the disease are obtained by using the theory of nonautonomous stochastic differential equations. Finally, numerical simulations are utilized to illustrate our theoretical analysis.

When multiple individuals interact in a conversation or as part of a large crowd, emergent structures and dynamics arise that are behavioral properties of the interacting group rather than of any individual member of that group. Recent work using traditional signal processing techniques and machine learning has demonstrated that global acoustic data recorded from a crowd at a basketball game can be used to classify emergent crowd behavior in terms of the crowd's purported emotional state. We propose that the description (...) of crowd behavior from such global acoustic data could benefit from nonlinear analysis methods derived from dynamical systems theory. Such methods have been used in recent research applying nonlinear methods to audio data extracted from music and group musical interactions. In this work, we used nonlinear analyses to extract features that are relevant to the behavioral interactions that underlie acoustic signals produced by a crowd attending a sporting event. We propose that recurrence dynamics measured from these audio signals via recurrence quantification analysis (RQA) reflect information about the behavioral dynamics of the crowd itself. We analyze these dynamics from acoustic signals recorded from crowds attending basketball games, and that were manually labeled according to the crowds' emotional state across six categories: angry noise, applause, cheer, distraction noise, positive chant, and negative chant. We show that RQA measures are useful to differentiate the emergent acoustic behavioral dynamics between these categories, and can provide insight into the recurrence patterns that underlie crowd interactions. (shrink)

In this paper we study the connection between the use of evaluative language and the building of both personal and social identities, from the perspective of Dynamical System Theory. We primarily discuss two issues: 1) The use of evaluation ) as a means to the construction of both individual and group identities, thus exploring how the connection between linguistic choices and social identities is shaped by interactional needs for stancetaking. In order to illustrate this connection, we examine examples of (...) the use of evaluative language in a web social network, and we analyze some of the discourse elements showing ways of positioning that act as catalysts for the emergence of a multifactorial dynamic system of identities. 2) The consideration of Dynamical System Theory as a theoretical framework for the modeling of language and identity. Although originally a mathematical theory, DST has been adopted by cognitive science as a valid framework for the study of cognitive phenomena, on the grounds that natural cognition is a dynamical phenomenon. Within the realm of linguistics and pragmatics, this study is to a certain degree in line with some recent studies such as Gibbs, Geeraerts, Kristiansen and Peirsman, or Moreno Fernández. Thus, we herein focus on how linguistic evaluation intervenes in the intricate dynamical system of identity, and even though we do not engage in complex mathematical disquisition, we argue that the idea and philosophical foundation underlying DST can lead us towards the ‘integration’ of the complex equation of identity construction, and that consequently the field has great potential for further research. (shrink)

Solvency assessment is the core content of insurance supervision. In this paper, from the perspective of capital flow, the insurance company’s capital flow is regarded as a dynamic system, the stochastic differential equations model is established to describe its flow characteristics, and the existence of positive equilibrium point of the system is proved, as well as the conditions of stability at equilibrium point, that is, the requirements of the insurance company’s solvency. Furthermore, by using the numerical simulation method, we get (...) the strategy of insurance companies to deal with the solvency shortage when facing the change of external environment, and the strategy of insurance company to deal with solvency shortage is obtained. (shrink)

The dynamics of calcium in the cortical cytoplasm of plant cells has been modeled by Goodwin & Trainor (1985) using a mechanochemical field theory based on the interaction between calcium ions and the cytoskeleton. The resulting mathematical model is a system of two non-linear partial differential equations which rule the evolution of the free calcium concentration and of the cytogel strain field in the cytoplasm. According to the values of parameters such as: calcium diffusion coefficient, strength of the calcium-strain coupling, (...) gel elasticity or total calcium concentration, this system may be stable or unstable around an homogeneous equilibrium state. With the aid of numerical simulations, various kinds of solutions have been observed. When inertial forces ar neglected or for low values of the gel density, most of the solutions are asymptotically stable and are reached after a more or less complex transient. But for higher values of the volumetric density more complex solutions may exist, periodic in time and space or eventually chaotic. (shrink)

This paper aims at investigating the dynamic characteristics of a microring driven by dual arch electrodes because they are basic elements of microelectrostatic motors. The dual arch electrodes surround the periphery of the microring and are arranged symmetrically to the center of the ring. The electrodes are fixed while the microring is flexible. The electrostatic force will deform the microring, while the deflection of the microring changes the gap between the microring and the electrodes, thereby changing the electrostatic force. Therefore, (...) this is an electromechanical coupling effect. The nonlinear partial-differential equation that governs the motion of the microring is derived based on thin shell theory. Then, based on the assumption of small deflection, the nonlinear governing equation is linearized by truncating the higher-order terms of the Taylor series expansion of the nonlinear electrostatic force. After that, the linearized governing equation is discretized into a set of ordinary differential equations using Galerkin method in which the mode shape functions of the ring are adopted. The influences of the structural damping of the microring and the span of the arch electrodes on the forced response and dynamical stabilities of the microring are investigated. The results show that the damping ratio has a great influence on the system instability during high-frequency excitation. The unstable region of the system can increase with the increase of the electrode span; the response amplitude can also be increased within a certain range. (shrink)

Major events of the cell cycle—DNA synthesis, mitosis and cell division—are regulated by a complex network of protein interactions that control the activities of cyclin‐dependent kinases. The network can be modeled by a set of nonlinear differential equations and its behavior predicted by numerical simulation. Computer simulations are necessary for detailed quantitative comparisons between theory and experiment, but they give little insight into the qualitative dynamics of the control system and how molecular interactions determine the fundamental physiological properties of cell (...) replication. To that end, bifurcation diagrams are a useful analytical tool, providing new views of the dynamical organization of the cell cycle, the role of checkpoints in assuring the integrity of the genome, and the abnormal regulation of cell cycle events in mutants. These claims are demonstrated by an analysis of cell cycle regulation in fission yeast. BioEssays 24:1095–1109, 2002. © 2002 Wiley‐Periodicals, Inc. (shrink)

The calcium signals regulate the production and secretion of many signaling molecules like inositol trisphosphate ( $$IP_{3}$$ ) and adenosine triphosphate (ATP) in various cells including pancreatic $$\beta$$ -cells. The calcium signaling mechanisms regulating $$IP_{3}$$, ATP and insulin responsible for various functions of $$\beta$$ -cells are still not well understood. Any disturbance in these mechanisms can alter the functions of $$\beta$$ -cells leading to diabetes and metabolic disorders. Therefore, a mathematical model is proposed by incorporating the reaction-diffusion equation for calcium (...) dynamics and a system of first-order differential equations for $$IP_{3}$$, ATP-production and insulin secretion with initial and boundary conditions. The model incorporates the temporal dependence of $$IP_{3}$$ -production and degradation, ATP production and insulin secretion on calcium dynamics in a $$\beta$$ -cell. The piecewise linear finite element method has been used for the spatial dimension and the Crank-Nicolson scheme for the temporal dimension to obtain numerical results. The effect of changes in source influxes and buffers on calcium dynamics and production of $$IP_{3}$$, ATP and insulin levels in a $$\beta$$ -cell has been analyzed. It is concluded that the dysfunction of source influx and buffers can cause significant variations in calcium levels and dysregulation of $$IP_{3}$$, ATP and insulin production, which can lead to various metabolic disorders, diabetes, obesity, etc. The proposed model provides crucial information about the changes in mechanisms of calcium dynamics causing proportionate disturbances in $$IP_3$$, ATP and insulin levels in pancreatic cells, which can be helpful for devising protocols for diagnosis and treatment of various metabolic diseases. (shrink)

In almost all of his early works Gilles Deleuze is concerned with one and the same problem: the problem of genesis. In response to this problem, Deleuze argues for a system of heterogenesis. In this article, I argue that Deleuze’s system of heterogenesis operates on three levels: (1) the differential multiplicity of virtual Ideas; (2) the implied multiplicity of intensive dramas; (3) the extensive and qualitative diversity of actual concepts. As I hope to show, the relation between these three levels (...) can be explained in terms of the logic of expression that Deleuze develops in 'Expressionism in Philosophy: Spinoza.' In this way, I hope to gain clarity without losing nuance. The rather technical and abstract language of expression will become more concrete and understandable when it is understood in terms of intensive dramas, virtual Ideas and actual concepts. At the same time, the three levels of expression make it possible to show how these notions are interlinked. Accordingly, this article is divided in four parts. In the first part, I will explain how Deleuze takes up Kant’s discovery of the principle of difference as a reaction against the model of representation. The second part focuses on the two multiplicities (virtual Ideas and intensive dramas) that produce diversity (actual concepts). In the third part, these two multiplicities are linked to each other with the help of the logic of expression that Deleuze derives from Spinoza. The fourth, concluding part will connect the logic of expression to the complex dynamic of difference and repetition. (shrink)

Excessive use of social media is a developing concern in the twenty-first century. This issue needs to be addressed before it has any more significant consequences than what we are currently experiencing. As a preventive technique, advertisements and awareness-raising campaigns about the detrimental impact of digital technologies are used. The application of novel mathematical techniques and terminologies in this field of study will have significant potential to enhance healthy living by preventing certain ailments. This is the most compelling justification for (...) conducting a new study with the most up-to-date techniques at our disposal. This study investigates clear and concise transmission in order to generate a deterministic mathematical model of social media addiction S M A using the fractal-fractional derivative operator. Also, the analysis of the S M A model in terms of the invariant domain, the existence of a positive invariant solution, and equilibria assumptions are stated in a detailed manner. Besides that, the basic reproduction number ℝ 0 < 1 is computed, demonstrating that the proposed methodology is more efficacious. The Atangana-Baleanu FF differential operators are recently defined in FF differential operators that are applied to characterize the S M A model’s mathematical algorithm. We investigated the numerical behaviour of the S M A in three ways: changing the fractional-order α as well as the fractal-dimension ℘ ; changing α while keeping ℘ constant; and changing ℘ while keeping α constant. Our examined visualizations and simulation studies using MATLAB for the numerical modelling of the aforementioned system showed that the novel developed Atangana-Baleanu FF differential operators produce remarkable results when compared to the classical frame. (shrink)

Precision medicine and molecular systems medicine (MSM) are highly utilized and successful approaches to improve understanding, diagnosis, and treatment of many diseases from bench-to-bedside. Especially in the COVID-19 pandemic, molecular techniques and biotechnological innovation have proven to be of utmost importance for rapid developments in disease diagnostics and treatment, including DNA and RNA sequencing technology, treatment with drugs and natural products and vaccine development. The COVID-19 crisis, however, has also demonstrated the need for systemic thinking and transdisciplinarity and the (...) limits of MSM: the neglect of the bio-psycho-social systemic nature of humans and their context as the object of individual therapeutic and population-oriented interventions. COVID-19 illustrates how a medical problem requires a transdisciplinary approach in epidemiology, pathology, internal medicine, public health, environmental medicine, and socio-economic modeling. Regarding the need for conceptual integration of these different kinds of knowledge we suggest the application of general system theory (GST). This approach endorses an organism-centered view on health and disease, which according to Ludwig von Bertalanffy who was the founder of GST, we call Organismal Systems Medicine (OSM). We argue that systems science offers wider applications in the field of pathology and can contribute to an integrative systems medicine by (i) integration of evidence across functional and structural differentially scaled subsystems, (ii) conceptualization of complex multilevel systems, and (iii) suggesting mechanisms and non-linear relationships underlying the observed phenomena. We underline these points with a proposal on multi-level systems pathology including neurophysiology, endocrinology, immune system, genetics, and general metabolism. An integration of these areas is necessary to understand excess mortality rates and polypharmacological treatments. In the pandemic era this multi-level systems pathology is most important to assess potential vaccines, their effectiveness, short-, and long-time adverse effects. We further argue that these conceptual frameworks are not only valid in the COVID-19 era but also important to be integrated in a medicinal curriculum. (shrink)

A new conceptual framework is proposed to situate and integrate the parallel theories of Turchin, Powers, Campbell and Simon. A system is defined as a constraint on variety. This entails a 2 × 2 × 2 classification scheme for “higher‐order” systems, using the dimensions of constraint, (static) variety, and (dynamic) variation. The scheme distinguishes two classes of metasystems from supersystems and other types of emergent phenomena. Metasystems are defined as constrained variations of constrained variety. Control is characterized as a (...) constraint exerted by a separate system. The emergence of hierarchical systems is motivated by evolutionary principles. The positive feedback between variety and constraint, which underlies the “branching growth of the penultimate level,” leads to the interpretation of metasystem transitions as phases of accelerated change in a continuous evolutionary progression toward increasing variety. The most important MSTs in the history of evolution are reinterpreted in this framework: mechanical motion, dissipative structuration, life, multicellular differentiation, sexuality, simple reflex, complex reflex, associating, thinking, metarationality and social interaction. (shrink)

This chapter presents an account of Merleau-Ponty’s interpretation of the body schema as an operative intentionality that is not only opposed to, but also complexly intermingled with, the representation-like grasp of the world and one’s own body, or the body image. The chapter reconstructs Merleau-Ponty’s position primarily based on his preparatory notes for his 1953 lecture ‘The Sensible World and the World of Expression’. Here, Merleau-Ponty elaborates his earlier efforts to show that the body schema is a perceptual ground against (...) which the perceived world stands out as a complex of perceptual figures. The chapter clarifies how Merleau-Ponty’s renewed interpretation of the figure-ground structure makes it possible for him to describe the relationship between body schema and perceptual (body) image as a strictly systematic phenomenon. Subsequently, the chapter shows how Merleau-Ponty understands apraxia, sleep, and perceptual orientation as examples of dedifferentiation and subtler differentiation of the body-schematic system. The last section clarifies how such body-schematic differentiating processes give rise to relatively independent superstructures of vision and symbolic cognition which constitute our body image. It, moreover, explains how, according to Merleau-Ponty, the cognitive superstructures always need to be supported by praxic operative intentionality to maintain their full sense, even though, in some cases, they have the power to compensate for praxic deficiencies. (shrink)

The frame/content theory of speech production is restricted to output mechanisms in the target article; we suggest that these ideas might best be viewed in the context of language production proceeding as a coordinated dynamical whole. The role of the medial premotor system in generating frames matches the important role it may play in the internally dependent timing of motor acts. The proposed coevolution of cortical architectonics and language production mechanisms suggests a significant divergence between primate and cetacean species (...) corresponding to major differences in areal differentiation trends in cerebral cortex. (shrink)

We contrast reactive and endogenously active perspectives on brain activity. Both have been pursued continuously in neurophysiology laboratories since the early 20thcentury, but the endogenous perspective has received relatively little attention until recently. One of the many successes of the reactive perspective was the identification, in the second half of the 20th century, of the distinctive contributions of different brain regions involved in visual processing. The recent prominence of the endogenous perspective is due to new findings of ongoing oscillatory activity (...) in the brain at a wide range of time scales, exploiting such techniques as single-cell recording, EEG, and fMRI. We recount some of the evidence pointing to ways in which this endogenous activity is relevant to cognition and behavior. Our major objective is to consider certain implications of the contrast between the reactive and endogenous perspectives. In particular, we relate these perspectives to two different characterizations of explanation in the new mechanistic philosophy of science. In a basic mechanistic explanation, the operations of a mechanism are characterized qualitatively and as functioning sequentially until a terminating condition is realized. In contrast, a dynamic mechanistic explanation allows for non-sequential organization and emphasizes quantitative modeling of the mechanisms's behavior. For example, with appropriate parameter values a set of differential equations can be used to demonstrate ongoing oscillations in a system organized with feedback loops. We conclude that the basic conception of mechanistic explanation is adequate for reactive accounts of brain activity, but dynamical accounts are required to explain sustained, endogenous activity. (shrink)

A new approach to developing formulisms of physics based solely on laws of mathematics is presented. From simple, classical statistical definitions for the observed space-time position and proper velocity of a particle having a discrete spectrum of internal states we derive u generalized Schrödinger equation on the space-time manifold. This governs the evolution of an N component wave function with each component square integrable over this manifold and is structured like that for a charged particle in an electromagnetic field but (...) also includes SU(N) gauge field couplings. This construction reveals a new hasis for gauge invariance and new insight into the appearance of spin and other such properties in relativistic quantum mechanics and suggests a new charged particle model. (shrink)

L. Hardy has formulated an axiomatization program of quantum mechanics and generalized probability theories that has been quite influential. In this paper, properties of typical Hamiltonian dynamical systems are used to argue that there are applications of probability in physical theories of systems with dynamical complexity that require continuous spaces of pure states. Hardy’s axiomatization program does not deal with such theories. In particular Hardy’s fifth axiom does not differentiate between such applications of classical probability and (...) quantum probability. (shrink)

The paper raises the theoretical question of the cultural mediational nature of literary intertexts from the point of view of generic and transformational dynamics. The intertextual complex as mediational operator is examined at two levels – (1) in the context of cultural diachrony by observing how the literary work establishes its place in the history of literature closely connected to the metapoiesis of the text; (2) at various kinds of intratextual interlevel movements regulating the evolution of a whole intertextual system (...) within the work. Differentiating the ontological, generative and transformational conceptualization of intertextual poetics, an attempt is made to define the basic textual modes of the pretext, the intext and the intertext by describing their functionality in the building of an intersemiotic literary system. The relevant functions are grasped by shedding light upon the types of the sign of which the given signifying structures consist (here a terminological clarification and re-evaluation are added) and their textual semantics in terms of referential and relational quality (cf. the different versions of referential and relational semantics). In the first place, however, the paper aims at outlining the structure and content of the generic-transformational semiotic processes in which the dynamic aspects of intertextual semiosis are revealed. Within this framework, the processuality of the development of the intertextual signifying structure iselucidated, shown as a chain of reciprocal sign activities resulting in constantly evolving semantic shifts within the intra- and intertextual semiosis processes, all relying on mediational operations. Text examples are taken from and references made to works by A. S. Pushkin, I. S. Turgenev, F. M. Dostoevsky and J. M. Coetzee. (shrink)

Nursing is possible owing to a series of intricate systemic relations. Building on an established tradition of sociological research, we critically analysed the nursing profession in Chile, with an emphasis on its education system, in the light of social systems theory. The paper's aim was to explore basic characteristics of nursing education as a system, so as to outline its current evolution. Drawing on recent developments in nursing, we applied an empirical framework to identify and discuss functionally differentiated (...) class='Hi'>systems that are relevant to nursing and observe communications between them. We found that the dynamics of nursing as a whole develop from communications with closely related systems, including the nursing profession and the education system more broadly. While the discipline (as a system of representations) strives to control the profession (as an applied occupational field), the necessities of practicing nurses imply other forces mediating the making of the profession, a process framed by market dynamics in education and health. (shrink)

The organization of the complex mixed-mode oscillations generated, in a three-dimensional variable space, by an autocatalytic process formalized as a cubic monomial is analyzed. The generation of the temporal patterns is elucidated by complementary approaches dealing with the three-variable differential continuous system itself and with successive discrete applications modelling its first return map. The extent to which the underlying bifurcation structures could constitute a fingerprint of autocatalytic processes is discussed in connection with the modelling of biological systems.

The purpose of this work is reviewing some reduction results to deal with systems of nonautonomous ordinary differential equations with two time scales. They could be included among the so-called approximate aggregation methods. The existence of different time scales in a system, together with some long-term features, are used to build up a simpler system governed by a lesser number of state variables. The asymptotic behavior of the latter system is then used to describe the asymptotic behaviour of the (...) former one. The reduction results are stated in two particular but important cases: periodic systems and asymptotically autonomous systems. The reduction results are illustrated with the help of simple spatial SIS epidemic models including either periodic or asymptotically autonomous terms. (shrink)

The present paper introduces "ontomimetic simulation" and argues that this class of models has enabled the investigation of hypotheses about complex systems in new ways that have epistemological relevance. Ontomimetic simulation can be differentiated from other types of modeling by its reliance on causal similarity in addition to representation. Phenomena are modeled not directly but via mimesis of the ontology (i.e. the "underlying physics", microlevel etc.) of systems and a subsequent animation of the resulting model ontology as a (...) dynamical system. While the ontology is clearly used for computing system states, what is epistemologically important is that it is viewed as a hypothesis about the makeup of the studied system. This type of simulation, where model ontologies are used as hypotheses, is here called inverse ontomimetic simulation since it reverses the typical informational path from the target to the model system. It links experimental and analytical techniques in being explicitly dynamical while at the same time capable of abstraction. Inverse ontomimetic simulation is argued to have a great impact on science and to be the tool for hypothesis-testing that has made systematic theory development for complex systems possible. (shrink)

A tight control of intracellular [Ca2+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{2+}$$\end{document}] is essential for the survival and normal function of cells. In this study we investigate key mechanistic steps by which calcium is regulated and calcium oscillations could occur using in silico modeling of membrane transporters. To do so we give a deterministic description of intracellular Ca2+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{2+}$$\end{document} dynamics using nonlinear dynamics in order to understand Ca2+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{2+}$$\end{document} signaling. We first present the ordinary differential equations system for cell calcium kinetics and make a preliminary work on Sobol indices. We then describe and analyze complex transporters action. Besides, we analyze the whole system. We finally perform numerical simulations and compare our results to real data. (shrink)

Dynamical systems theory (DST) is a branch of mathematics that assesses abstract or physical systems that change over time. It has a quantitative part (mathematical equations) and a related qualitative part (plotting equations in a state space). Nonlinear dynamical systems theory applies the same tools in research involving phenomena such as chaos and hysteresis. These approaches have provided different ways of investigating and understanding cognitive systems in cognitive science and neuroscience. The ‘dynamical hypothesis’ (...) claims that cognition is and can be understood as dynamical systems. Common consequences for such an approach include rejecting understanding cognition as information processing in nature, including eschewing explanatory roles for computation or representation. Contemporary applications of DST include mouse‐tracking studies in cognitive science and nonrepresentational perspectives on motor control in neuroscience. Such work has philosophical implications concerning the boundaries of cognition, explanation, and representations. DST offers powerful methodology and theories that raise many topics of philosophical significance. (shrink)

The paper raises the theoretical question of the cultural mediational nature of literary intertexts from the point of view of generic and transformational dynamics. The intertextual complex as mediational operator is examined at two levels – (1) in the context of cultural diachrony by observing how the literary work establishes its place in the history of literature closely connected to the metapoiesis of the text; (2) at various kinds of intratextual interlevel movements regulating the evolution of a whole intertextual system (...) within the work. Differentiating the ontological, generative and transformational conceptualization of intertextual poetics, an attempt is made to define the basic textual modes of the pretext, the intext and the intertext by describing their functionality in the building of an intersemiotic literary system. The relevant functions are grasped by shedding light upon the types of the sign of which the given signifying structures consist (here a terminological clarification and re-evaluation are added) and their textual semantics in terms of referential and relational quality (cf. the different versions of referential and relational semantics). In the first place, however, the paper aims at outlining the structure and content of the generic-transformational semiotic processes in which the dynamic aspects of intertextual semiosis are revealed. Within this framework, the processuality of the development of the intertextual signifying structure iselucidated, shown as a chain of reciprocal sign activities resulting in constantly evolving semantic shifts within the intra- and intertextual semiosis processes, all relying on mediational operations. Text examples are taken from and references made to works by A. S. Pushkin, I. S. Turgenev, F. M. Dostoevsky and J. M. Coetzee. (shrink)

Multi-level discrete models of genetic networks, or the more general piecewise affine differential models, provide qualitative information on the dynamics of the system, based on a small number of parameters (such as synthesis and degradation rates). Boolean models also provide qualitative information, but are based simply on the structure of interconnections. To explore the relationship between the two formalisms, a piecewise affine differential model and a Boolean model are compared, for the carbon starvation response network in E. coli . The (...) asymptotic dynamics of both models are shown to be quite similar. This study suggests new tools for analysis and reduction of biological networks. (shrink)

We show that dynamical clustering, where a system segregates into distinguishable subsets of synchronized elements, and chimera states, where differentiated subsets of synchronized and desynchronized elements coexist, can emerge in networks of globally coupled robust-chaos oscillators. We describe the collective behavior of a model of globally coupled robust-chaos maps in terms of statistical quantities and characterize clusters, chimera states, synchronization, and incoherence on the space of parameters of the system. We employ the analogy between the local dynamics of a (...) system of globally coupled maps with the response dynamics of a single driven map. We interpret the occurrence of clusters and chimeras in a globally coupled system of robust-chaos maps in terms of windows of periodicity and multistability induced by a drive on the local robust-chaos map. Our results show that robust-chaos dynamics does not limit the formation of cluster and chimera states in networks of coupled systems, as it had been previously conjectured. (shrink)