Complex dynamical systems theory is an evolution of nonlinear dynamics, developed for modeling and simulation of biological systems. Here, we speculate on the potential of this strategy for the emerging theory of social systems, and the implications for the future of our own planetary society.

This work presents a post-positivist research framework for explaining any surprising or anomalous fact in the evolutionary path of a complex, dynamic, and contingent social process. Firstly, it elaborates on the reconciliation betweenthe ontological and epistemological assumptions of Critical Realism with the principles of American Pragmatism. Next, the research method is presented: theoretical propositions about a social structure are translated into a set of grammar rules that acknowledge patterns of sequences of events, either involving individual action or interaction between (...) actors within a real social system. The result is a discrete mathematical model for a concrete category of social process based on these rules. Finally, data-grounded refinement of the theory is possible through comparison between cases belonging to the same category, but differing in some contingent pattern of sequences of event outcomes. Consequently, their grammars differ in some pairs of context-sensitive rules that explain this surprising fact, and the derivation of this alternative historical trajectory of event outcomes becomes an extension to the early category of social process. In this sense, the proposed framework suggests a hierarchy of classes of grammars for middle-range explanations based on the ontological assumption of the generative nature of social reality. (shrink)

Unified and causal complex-dynamic origin of standard (special and general) relativistic and quantum effects revealed previously at the lowest levels of world interaction dynamics is explicitly generalised to all higher levels of unreduced interaction processes, thus additionally confirming the causally complete character of complex-dynamical, naturally quantised relativity, which does not contain any artificially added, abstract postulates. We demonstrate some elementary applications of this generalised quantum relativity at higher levels of complex brain and social interaction dynamics.

Systemic therapy considers the complex dynamics of relational factors and resources contributing to psychological symptoms. Negative maintaining factors have been well researched for people suffering from Alcohol-use Disorders. However, we know little about the complex dynamics of these negative factors and resources. We interviewed fifty-five participants suffering or fully remitted from Alcohol-use disorders in this cross-sectional study. The interviews focused on relational factors referring to a Support Social Network and a Craving Social Network. The CSN included (...) all significant others who were associated with craving situations. We compared the network characteristics of the group suffering from Alcohol-use Disorders to a fully remitted control group. The abstinent group with full remission named on average fewer individuals in the CSNs. They had lower social negativity mean scores in the Support Social Network compared to the non-remitted group. In the CSN, the mean scores of social support were significantly higher than the median for both groups. These findings reveal the complex interplay of relational patterns contributing to the etiology, maintenance, and recovery from Alcohol-use disorders. A successful recovery can be linked to increased social resources and reduced relations associated with craving. However, craving-associated relations represent an important source of social support. Future research should investigate this ambivalence for the systemic perspective on the explanation and treatment of Alcohol-use disorders. (shrink)

A generalization of a Burridge-Knopoff spring-block model is investigated to illustrate the dynamics of transform faults. The model can undergo Hopf bifurcation and fold bifurcation of limit cycles. Considering the cyclical nature of the spring stiffness, the model with periodic perturbation is further explored via a continuation technique and numerical bifurcation analysis. It is shown that the periodic perturbation induces abundant dynamics, the existence, the switch, and the coexistence of multiple attractors including periodic solutions with various periods, quasiperiodic (...) solutions, chaotic solutions through torus destruction, or cascade of period doublings. Throughout the results obtained, one can see that the system manifests complex dynamical behaviors such as chaos, self-organized criticality, and the transition of dynamical behaviors when it comes to periodic perturbations. Even very small variation of a parameter can result in radical changes of the dynamics, which provides a new insight into the fault dynamics. (shrink)

distraction that leads innocent Post Keynesians into “classical sin.” Davidson (1994, 1996) argues that core Post Keynesian (PK) ideas such as that insufficient aggregate demand arise from fundamental uncertainty in a monetary economy do not depend on nonlinearity or complexity, that these core concepts are axiomatically and ontologically true, and that the inability of agents to forecast well in dynamically complex situations reflects mere epistemological problems of insufficient computational abilities. Thus complex dynamics is merely a classical stalking (...) horse. This writer (Rosser, 1990, 1998, 2001) disagrees with the argument presented above and its relatives (Mirowski, 1990; Carrier, 1993). Dynamic complexity provides a foundation for fundamental uncertainty in Keynesian and PK models, and this applies to most of the various sub-branches of PKE besides Davidson’s “fundamentalist” or “Keynes-Post Keynesian”2 approach. The argument will be considered regarding three subdivisions of Post Keynesianism as identified by Hamouda and Harcourt (1988): the aforementioned fundamentalist Keynesianism, Sraffian (or neo-Ricardian), and Kaleckian (or Kaleckian- Robinsonian).3 Following King (2002, chap. 10), I admit to being more in sympathy with those he describes as “synthesizers” than with the more partisan sectarians of these approaches.4 I shall describe how each sub-branch has been analyzed using ideas of.. (shrink)

This paper presents a view of the process of transition from planned command socialism to mixed market capitalism involving nonlinear complex dynamical phenomena. After the former institutional structure disappears a coordination failure can bring about macroeconomic collapse as in almost all of the former Soviet bloc or macroeconomic boom as in China. A closely linked phenomenon is the rise of the underground economy as inflation and income inequality increase. This can lead to a jump from one equilibrium to a (...) very different one as nonlinear social feedback processes operate in the transition. (shrink)

This paper presents a view of the process of transition from planned command socialism to mixed market capitalism involving nonlinear complex dynamical phenomena. After the former institutional structure disappears a coordination failure can bring about macroeconomic collapse as in almost all of the former Soviet bloc or macroeconomic boom as in China. A closely linked phenomenon is the rise of the underground economy as inflation and income inequality increase. This can lead to a jump from one equilibrium to a (...) very different one as nonlinear social feedback processes operate in the transition. (shrink)

According to resource limitation, a more realistic pest management is that the impulsive control actions should be adjusted according to the densities of both pest and natural enemy in the field, which result in nonlinear impulsive control. Therefore, we have proposed a Beddington–DeAngelis interference predator-prey model concerning integrated pest management with both density-dependent pest and natural enemy population. We find that the pest-eradication periodic solution is globally stable if the impulsive period is less than the critical value by Floquet theorem. (...) The condition of permanent is established, and a stable positive periodic solution appears via a supercritical bifurcation by bifurcation theorem. Finally, in order to investigate the effects of those nonlinear control strategies on the successful pest control, the bifurcation diagrams showed that the model exists with very complex dynamics. Consequently, the resource limitation may result in pest outbreak in complex ways, which means that the pest control strategies should be carefully designed. (shrink)

In this paper, a fresh shear-displacement model is developed for the plastic deformation of the bulk metallic glasses. The multiscale behavior in the shear banding process and the dynamics transition with the parameters are investigated in analytical form. We present a theoretical support for the transition from unstable states to stable states in the experiment by multiscale analysis and the stability analysis. With the small parameter increasing from negative to positive, the stability of the shear slipping displacement system changes, (...) and there is a limit cycle at the transition stage. Meanwhile, the phase diagram and the power spectrum also suggest that there is dynamics transition with the parameter changing. Moreover, the complexity is analyzed for different disturbance parameters, and it is coincident with the fact that the solution is more irregular for larger disturbance. In addition, we find that the amplitude of solution decreases with the temperature decreasing, which is consistent with the experimental results that the amplitude of the serration is smaller and smaller as the temperature decreases. (shrink)

An extended analysis compared to observations shows that modern “globalised” world civilisation has passed through the invisible “complexity threshold”, after which usual “spontaneous”, empirically driven kind of development (“invisible hand” etc.) cannot continue any more without major destructive tendencies. A much deeper, non-simplified understanding of real interaction complexity is necessary in order to cope with such globalised world development problems. Here we introduce the universal definition, fundamental origin, and dynamic equations for a major related quantity of (systemic) risk characterising real (...) complex system development tendencies at any level of dynamics. Practically important conclusions are derived, opening further detailed applications in economy, finance and development practice. (shrink)

The theory of nonlinear complex systems has become a successful and widely used problem-solving approach in the natural sciences - from laser physics, quantum chaos and meteorology to molecular modeling in chemistry and computer simulations of cell growth in biology. In recent times it has been recognized that many of the social, ecological and political problems of mankind are also of a global, complex and nonlinear nature. And one of the most exciting topics of present scientific and public (...) interest is the idea that even the human mind is governed largely by the nonlinear dynamics of complex systems. In this wide-ranging but concise treatment Prof. Mainzer discusses, in nontechnical language, the common framework behind these endeavours. Special emphasis is given to the evolution of new structures in natural and cultural systems and it is seen clearly how the new integrative approach of complexity theory can give new insights that were not available using traditional reductionistic methods. (shrink)

The contemporary process of financialization has been a major driver of the remarkable changes witnessed in global food and agricultural markets over the past decade, contributing to the rise and subsequent volatility of food and agricultural commodity prices since 2006. In the wake of these developments it has become clear that the turmoil has intensified the relationship between agriculture and finance in ways that have profound and enduring implications for the sector, and the people whose lives and livelihoods depend upon (...) it. This symposium brings together four original research articles that contemplate the contemporary relationship between the agrifood and financial sectors. They examine a variety of overlapping themes, including the creation of financial assets from farmland and agricultural commodities, the activities of different types of investors in these assets in specific geographic contexts, and the challenges of governing this activity at the global scale. These articles show that the period of market volatility that began a decade ago re-invigorated investor interest in financial products linked to agriculture and farming, and inspired the packaging of new forms of financial assets in ways that have affected politics and practice on the ground, and are likely to leave a lasting legacy. (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.

This paper describes a traditional SIR type epidemic model with saturated infection rate and treatment function. The dynamics of the model is studied from the point of view of stability and bifurcation. Basic reproduction number is obtained and it is shown that the model system may possess a backward bifurcation. The global asymptotic stability of the endemic equilibrium is studied with the help of a geometric approach. Optimal control problem is formulated and solved. Some numerical simulation works are carried (...) out to validate our analytical results. (shrink)

“A Public Domain, once a velvet carpet of rich buffalo-grass and grama, now an illimitable waste of rattlesnake-bush and tumbleweed, too impoverished to be accepted as a gift by the states within which it lies. Why? Because the ecology of the Southwest happened to be set on a hair trigger.”.

(This version was submitted to Behavioral and Brain Science. A revised version was published by Biological Theory) Estimates of autism’s incidence increased 5-10 fold in ten years, an increase which cannot be genetic. Though many mutations are associated with autism, no mutation seems directly to cause autism. We need to find the direct cause. Complexity science provides a new paradigm - confirmed in biology by extensive hard data. Both the body and the personality are complex dynamic systems which spontaneously (...) self-organize from simple dynamic systems. Autism may therefore be caused by the failure of a simple dynamic system. We know that infants who cannot track their mother’s face often become autistic, that eye-contact initiates intersubjectivity which is blocked in autism, and that the infant-mother pair seems designed to promote eye-contact, as does the eye’s appearance. This author earlier proposed that failure of eye-contact might directly cause autism and that early non-maternal childcare, including television/video, would therefore be statistically linked to autism. Waldman et al. (2008; 2006) recently proved that autism is strongly linked to precipitation (indoor activity) and to the introduction of cable. The most plausible explanation? Early exposure to television/video is linked to autism. Furthermore a normal developmental cascade (blocked in autism) has been deciphered: (a) Infant-mother eye-contact triggers increased maternal attention. (b) Early maternal attention permanently increases not only baseline vasopressin but also that oxytocin release which is triggered by subsequent maternal attention. (c) Vasopressin and oxytocin promote face recognition, gazing-at-the-eyes, emotion recognition, and social bonding. The eye-contact hypothesis suggests a clinical study addressing prevention: recruit prospective parents who agree to curtail television/video/computer/wi-fi in their families; measure autism’s incidence in their children. (shrink)

Over the past half century, I have been developing and defending a libertarian view of free will that is incompatible with determinism. In the past decade, I have made changes to this view in response to the large critical literature that has developed around it since the publication of my book The Significance of Free Will (Oxford University Press, 1996). This paper describes and defends some of the more significant of these new aspects of my view. Section 1 describes the (...) problem of free will as conceived traditionally and in modern times, as well as the various competing positions on it (compatibilist, libertarian, skeptical, and so forth). In section 2 I concede to compatibilists that there are many meanings of freedom, and that many of them could exist in a thoroughly determined world. But there is one kind of traditional freedom, I argue, that could not exist in a thoroughly determined world—freedom of will. Sections 3 and 4 explain what this freedom of will requires and why it is important. Sections 5–11 then discuss and answer many arguments that have been made against the possibility of such a free will requiring indeterminism. (shrink)

Psychological research has generally suffered from methodological fundamentalism, which is an overly strict interpretation of what is considered “scientific” and has created a psychology of triviality. Methodological fundamentalism often constricts the study of a complex dynamic psychology that encompasses both observed and unobserved reality with interacting and interdependent variables. In Against Method, Feyerabend (1993) posits there could be no set scientific method and that great scientists are methodological opportunists who use any methodology that helps with discovery. As opposed to (...) Fisher’s (1925) arbitrary, categorical standard of p<.05, I suggest as a strength of a scientific finding the review of confidence levels of across various populations, methods, measures and forms of analyses. Eventually, I hope that an unbiased computer analysis of studies can guide researchers as to what theories show high confidence levels across various populations, methods, measures and forms of analyses and suggest the next step to advance the science. (shrink)

Spatial predator-prey models have been studied by researchers for many years, because the exact distributions of the population can be well illustrated via pattern formation. In this paper, amplitude equations of a spatial Holling–Tanner predator-prey model are studied via multiple scale analysis. First, by amplitude equations, we obtain the corresponding intervals in which different kinds of patterns will be onset. Additionally, we get the conclusion that pattern transitions of the predator are induced by the increasing rate of conversion into predator (...) biomass. Specifically, pattern transitions of the predator between distinct Turing pattern structures vary in an orderly manner: from spotted patterns to stripe patterns, and finally to black-eye patterns. Moreover, it is discovered that pattern transitions of prey can be induced by cross-diffusion; that is, patterns of prey transmit from spotted patterns to stripe patterns and finally to a mixture of spot and stripe patterns. Meanwhile, it is found that both effects of cross-diffusion and interaction between the prey and predator can lead to the complicated phenomenon of dynamics in the system of biology. (shrink)

One of the most efficient predator-prey models with spatial effects is the one with ratio-dependent functional response. However, there is a need to further explore the effects of spatial motion on the dynamic behavior of population. In this work, we study a ratio-dependent predator-prey model with diffusion terms. The aim of this work is to investigate the changes in predator’s distribution in space as the prey populations change their mobility. We observe that the frequency diffusion of the prey gives rise (...) to the sparse density of the predator. Moreover, we also observe that the increasing rate of the conversion into predator biomass induces pattern transitions of the predator. Specifically speaking, Turing pattern of the predator populations goes gradually from a spotted pattern to a black-eye pattern, with the intermediate state being the mixture of spot and stripe pattern. The simulation results and analysis of this work illustrate that the diffusion rate and the real intrinsic factor influence the persistence of the predator-prey system mutually. (shrink)

Complexity arises from interaction dynamics, but its forms are co-determined by the operative constraints within which the dynamics are expressed. The basic interaction dynamics underlying complex systems is mostly well understood. The formation and operation of constraints is often not, and oftener under appreciated. The attempt to reduce constraints to basic interaction fails in key cases. The overall aim of this paper is to highlight the key role played by constraints in shaping the field of (...) class='Hi'>complex systems. Following an introduction to constraints, the paper develops the roles of constraints in specifying forms of complexity and illustrates the roles of constraints in formulating the fundamental challenges to understanding posed by complex systems. (shrink)

Fishery dynamics are considered within the context of an integrated ecologiceconomic, or bioeconomic, approach. The possibility of complex dynamics is examined, both of the chaotic as well as the catastrophic variety. Issues involving learning and convergence by fishers are considered. Complications arising from multi-species interactions are considered as are complications arising from the hierarchical nature of fisheries. Policy responses to these problems are seen to involve the precautionary..

This paper presents a stylized overview of the process of transition from planned command socialism to mixed market capitalism in stages, each involving nonlinear complex dynamical phenomena. The end of the command form arises out of a chaotic hysteretic long wave investment cycle. After the former institutional structure disappears a coordination failure brings about macroeconomic collapse. As recovery emerges various complex fluctuations of employment appear as government labor policies oscillate.

This paper investigates a stochastic two-patch predator-prey model with ratio-dependent functional responses. First, the existence of a unique global positive solution is proved via the stochastic comparison theorem. Then, two different methods are used to discuss the long-time properties of the solutions pathwise. Next, sufficient conditions for extinction and persistence in mean are obtained. Moreover, stochastic persistence of the model is discussed. Furthermore, sufficient conditions for the existence of an ergodic stationary distribution are derived by a suitable Lyapunov function. Next, (...) we apply the main results in some special models. Finally, some numerical simulations are introduced to support the main results obtained. The results in this paper generalize and improve the previous related results. (shrink)

This paper investigates the exponential synchronization of complex dynamical networks based on the sampled-data control method. The sampled-data control means that the control input remains unchanged for a long time after each sampling, which can reduce the sampling number. By using the stability theory of the dynamical systems, this paper provides a novel sampling controller and estimates the bound of the sampling interval. Finally, a numerical example is given to demonstrate the effectiveness of the proposed design technique.

This article discusses the role of moment-to-moment affect dynamics in mental disorder and aims to integrate recent literature on this topic in the context of complex dynamical system theory. First, we will review the relevance of temporal and contextual aspects of affect dynamics in relation to psychopathology. Related to this, we will discuss recent insights resulting from a network view on affect dynamics in psychopathology. Next, we explore how we can reconcile literature findings from a perspective (...) of complex dynamical system theory. Finally, future directions with regard to personalized assessment of risk and diagnostic use are discussed. (shrink)

Cramer et al.'s article is an example of the fruitful application of complex dynamic systems theory. We extend their approach with examples from our own work on development and developmental psychopathology and address three issues: (1) the level of aggregation of the network, (2) the required research methodology, and (3) the clinical and educational application of dynamic network thinking.

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)

The current study explores the effects of a brief training program on complex problem solving (CPS) and dynamic decision making (DDM) performance in two computer-simulated tasks with different task characteristics, ChocoFine (N = 76) and WinFire (N = 99). Half of the participants in each simulation group received a brief training on 16 frequent CPS and DDM errors. We hypothesized that participants who received the training in errors would show better performance, report fewer errors, and show fewer behavioral errors (...) compared to those who did not receive the error training prior to the start of the simulated tasks. The results showed that participants in both training groups had better performance scores. Participants in the training condition reported fewer self-reported errors compared to the no-training group only in the ChocoFine simulation. Regarding behavioral errors, status-quo bias was related to weaker performance in both simulations. These findings have implications for leaders who are prone for the status-quo bias and for organizations which could implement trainings programs for DDM and CPS. (shrink)

The mathematical approach to such essentially biological phenomena as perseverative reaching is most welcome. To extend these results and make them more accurate, levels of analysis and neural centers should he distinguished. The navigational nature of sensorimotor control should be characterized more clearly, including the continuous dynamics of neural processes hut not limited to it. In particular, discrete conditions should be formalized mathematically as part of the biological process.

Aesthetic responsivity and the phenomenology of arts processes reflect integrative self-world engagements, and are informative about the nature of the world and our biology in ways that are often not be made evident through scientific research. Akins’ and Hahn’s research regarding human trichromatic visual perception brings together the art of photography, neuroscience, and psychophysics, along with analyses of perspectives on vision in science and philosophy, to invoke anti-reductive, holistic understandings of how we see colour. We bring aesthetics and the phenomenology (...) of arts processes to bear in exploring creaturely re-sponsivity to the complex inter-relational dynamics of light perception, and o˙er reflective metaphors for human engagements that challenge Darwinian utilitarian conceptions. We argue that attending to aesthetic and phenomenological aspects of experiences is essential to understanding how the shared circuits of cognition and sensory-motor engagement shape our perceptive responsive interactions. (shrink)

This chapter describes the application of reduction concepts in emergence and self organization of complex dynamical system. Condition-dependent laws compress and dynamical equation sets provide implicit compressed representations even when most of that information is not explicitly available without decompression. And, paradoxically, there is still the determined march of fundamental analytical dynamics expanding its compression reach toward a Theory of Everything—even while the more rapidly expanding domain of complex systems dynamics confronts its assumptions and its monolithicity. (...) Nor does science fall apart into a disunified aggregate of particular cases since, with fundamental dynamics as a backbone, complex matching up of models across theoretical and empirical domains then articulates its model-structured skeleton. Discussion provides the delicately entwined dance of emergence and reduction providing constraints on compression that also permit its expansion. However, while the vision is not dead, it is currently substantially more complexly structured through model similarities and differences than that initially envisaged and individuals are left with deep questions about compression unresolved. (shrink)