This paper investigates the diffusive predator-prey system with nonmonotonic functional response and fear effect. Firstly, we discussed the stability of the equilibrium solution for a corresponding ODE system. Secondly, we established a priori positive upper and lower bounds for the positive solutions of the PDE system. Thirdly, sufficient conditions for the local asymptotical stability of two positive equilibrium solutions of the system are given by using the method of eigenvalue spectrum analysis of linearization operator. Finally, the existence (...) and nonexistence of nonconstant positive steady states of this reaction-diffusion system are established by the Leray–Schauder degree theory and Poincaré inequality. (shrink)

In order to achieve flexible and smooth walking, we must accomplish subtasks (e.g., loading response, forward propulsion or swing initiation) within a gait cycle. To evaluate subtasks within a gait cycle, the analysis of muscle synergies may be effective. In the case of walking, extracted sets of muscle synergies characterize muscle patterns that relate to the subtasks within a gait cycle. Although previous studies have reported that the muscle synergies of individuals with disorders reflect impairments, a way to investigate the (...) instability in the activations of muscle synergies themselves has not been proposed. Thus, we investigated the local dynamic stability and orbital stability of activations of muscle synergies across various walking speeds using maximum Lyapunov exponents and maximum Floquet multipliers. We revealed that the local dynamic stability in the activations decreased with accelerated walking speeds. Contrary to the local dynamic stability, the orbital stability of the activations was almost constant across walking speeds. In addition, the increasing rates of maximum Lyapunov exponents were different among the muscle synergies. Therefore, the local dynamic stability in the activations might depend on the requirement of motor output related to the subtasks within a gait cycle. We concluded that the local dynamic stability in the activation of muscle synergies decrease as walking speed accelerates. On the other hand, the orbital stability is sustained across broad walking speeds. (shrink)

In this paper, we put forward a time-delay ecological competition system with food restriction and diffusion terms under Neumann boundary conditions. For the case without delay, the conditions for local asymptotic stability and Turing instability are constructed. For the case with delay, the existence of Hopf bifurcation is demonstrated by analyzing the root distribution of the corresponding characteristic equations. Furthermore, by using the normal form theory and the center manifold reduction of partial functional differential equations, explicit formulas (...) are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Finally, some simulation examples are provided to substantiate our analysis. (shrink)

In this study, for COVID-19, we divide people into four categories: susceptible S t, closely contacted C t, infective I t, and removed R t according to the current epidemic situation and then investigate two models: the SCIR models with immigration and without immigration. For the former, Model 1, we obtain the condition for global stability of its disease-free equilibrium. For the latter, Model 2, we establish the local asymptotic stability of its endemic equilibrium by constructing (...) Lyapunov function. Afterwards, by the bifurcation theory, we qualitatively analyze the properties of its Hopf bifurcations of the latter. Finally, numerical simulations are given to illustrate the obtained results of two models. The results imply the importance of finding closely contacted and overseas imports on epidemic control. It indicates that not only the incubation delay τ is crucial for the containment of the COVID-19 but also the scientific and rigorous containment measures are the key factors of the success of the containment. (shrink)

We consider the extent to which one can compute bounds on the rate of convergence of a sequence of ergodic averages. It is not difficult to construct an example of a computable Lebesgue measure preserving transformation of [0, 1] and a characteristic function f = χA such that the ergodic averages Anf do not converge to a computable element of L2([0, 1]). In particular, there is no computable bound on the rate of convergence for that sequence. On the other hand, (...) we show that, for any nonexpansive linear operator T on a separable Hilbert space and any element f , it is possible to compute a bound on the rate of convergence of Anf from T , f , and the norm f ∗ of the limit. In particular, if T is the Koopman operator arising from a computable ergodic measure preserving transformation of a probability space X and f is any computable element of L2 (X ), then there is a computable bound on the rate of convergence of the sequence Anf. (shrink)

Quantum mechanics is troubled by the problem of nonlocality inherent in the theory. In a series of papers we explore the possibility of an algebraic formulation of quantum mechanics based on local observables which would incorporate nonlocality when small distances are involved but would be separable at large distances. This paper reviews some of the basic ideas and theories developed recently. These include a unified localization scheme, the introduction of local comoving evolution, local comoving observables, and related (...) conservation laws. Technical considerations and mathematical jargon are kept to a minimum to avoid obscuring physical reasoning. (shrink)

This paper is concerned with the formulation and analysis of an epidemic model of COVID-19 governed by an eight-dimensional system of ordinary differential equations, by taking into account the first dose and the second dose of vaccinated individuals in the population. The developed model is analyzed and the threshold quantity known as the control reproduction number R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}_{0}$$\end{document} is obtained. We investigate the equilibrium stability of the system, and the COVID-free (...) equilibrium is said to be locally asymptotically stable when the control reproduction number is less than unity, and unstable otherwise. Using the least-squares method, the model is calibrated based on the cumulative number of COVID-19 reported cases and available information about the mass vaccine administration in Malaysia between the 24th of February 2021 and February 2022. Following the model fitting and estimation of the parameter values, a global sensitivity analysis was performed by using the Partial Rank Correlation Coefficient (PRCC) to determine the most influential parameters on the threshold quantities. The result shows that the effective transmission rate (α)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha )$$\end{document}, the rate of first vaccine dose (ϕ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\phi )$$\end{document}, the second dose vaccination rate (σ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\sigma )$$\end{document} and the recovery rate due to the second dose of vaccination (η)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\eta )$$\end{document} are the most influential of all the model parameters. We further investigate the impact of these parameters by performing a numerical simulation on the developed COVID-19 model. The result of the study shows that adhering to the preventive measures has a huge impact on reducing the spread of the disease in the population. Particularly, an increase in both the first and second dose vaccination rates reduces the number of infected individuals, thus reducing the disease burden in the population. (shrink)

To date, our knowledge of Rift Valley fever disease spread and maintenance is still limited, as flooding, humid weather and presence of biting insects such as mosquitoes, have not completely explained RVF outbreaks. We propose a model that includes livestock, mosquitoes and ticks compartments structured according to their questing and feeding behaviour in order to study the possible role of ticks on the dynamics of RVF. To quantify disease transmission at the initial stage of the epidemic, we derive an explicit (...) formula of the basic reproductive number, $$R_0$$ R 0. Using the concept of Metzler matrix, we state necessary conditions for global asymptotic stability of the disease-free equilibrium. Results suggest that although host-ticks interactions may serve as disease reservoirs or disease amplifiers, the Aedes reproductive number should be kept under unity if disease post-epizootics activities are to be controlled. Results of both local and global sensitivity analysis of selected model parameters indicate that $$R_0$$ R 0 is more sensitive to the ticks attachment and detachment rates, probability of transmission from ticks to host and from host to ticks, length of infection in livestock and ticks death rate. Furthermore, when comparing the mean value of $$R_0$$ R 0 with that from previous studies which did not include ticks we found that our $$R_0$$ R 0 is very much larger resulting in an increase in the exponential phase of an outbreak. These findings suggest that if ticks are capable of transmitting the virus, they may be contributing to disease outbreaks and endemicity. (shrink)

A nonlinear differential equation model is proposed to study the dynamics of HIV/AIDS and its effects on workforce productivity. The disease-free equilibrium point of the model is shown to be locally asymptotically stable when the associated basic reproduction number $$\mathcal{{R}}_{0}$$ is less than unity. The model is also shown to exhibit multiple endemic states for some parameter values when $$\mathcal{{R}}_{0} 1$$. Global asymptotic stability of the disease-free equilibrium is guaranteed only when the fractions of the Susceptible subclass populations (...) are within some bounds. Optimal control analysis of the model revealed that the most cost effective strategy that should be adopted in the fight against HIV/AIDS spread within the workforce is one that seeks to prevent infections and the treatment of infected individuals. (shrink)

The behavior of two-dimensional coupled map lattices is studied with respect to the global stabilization of unstable local fixed points without external control. It is numerically shown under which circumstances such inherent global stabilization can be achieved for both synchronous and asynchronous updating. Two necessary conditions for inherent global stabilization are derived analytically.

This essay examines the problems associated with the installation of a precision instrument at the National Astronomical Observatory of Chile, starting before its construction and following the process through its installation to its later useful life. Between 1908 and 1913, the director of the observatory, Friedrich W. Ristenpart, corresponded with the German manufacturer, A. Repsold & Söhne in Hamburg, trying to identify the critical points pertinent to the installation of the instrument in Chile. These communications reveal how the installation of (...) the instrument required the stabilization of local knowledge (location, adjustment, calibration, and staging) that would allow the data it obtained to be universally validated. This correspondence between user and manufacturer also reveals that the phenomenon of the mobility of instruments implies much more than simply transporting something from one place to another: there is no movement without some type of coordination between the extraction of an object from a certain place and context and its insertion into a new place and set of relationships. (shrink)

One method to determine the asymptotics of particular solutions of a difference equation is by solving an associated asymptotic functional equation. Here we study the behaviour of the solutions in an asymptotic neighbourhood of such individual solutions. We identify several types of attraction and repulsion, which range from almost orthogonality to almost parallelness. Necessary and sufficient conditions for these types of behaviour are given.

Grossberg and VanDieren have started a program to develop a stability theory for tame classes. We name some variants of tameness and prove the following. Let K be an AEC with Löwenheim-Skolem number ≤κ. Assume that K satisfies the amalgamation property and is κ-weakly tame and Galois-stable in κ. Then K is Galois-stable in κ⁺ⁿ for all n<ω. With one further hypothesis we get a very strong conclusion in the countable case. Let K be an AEC satisfying the amalgamation (...) property and with Löwenheim-Skolem number ℵ₀ that is ω-local and ℵ₀-tame. If K is ℵ₀-Galois-stable then K is Galois-stable in all cardinalities. (shrink)

The problem of stability in population dynamics concerns many domains of application in demography, biology, mechanics and mathematics. The problem is highly generic and independent of the population considered (human, animals, molecules,…). We give in this paper some examples of population dynamics concerning nucleic acids interacting through direct nucleic binding with small or cyclic RNAs acting on mRNAs or tRNAs as translation factors or through protein complexes expressed by genes and linked to DNA as transcription factors. The networks made (...) of these interactions between nucleic acids (considered respectively as edges and nodes of their interaction graph) are complex, but exhibit simple emergent asymptotic behaviours, when time tends to infinity, called attractors. We show that the quantity called attractor entropy plays a crucial role in the study of the stability and robustness of such genetic networks. (shrink)

even if an equilibrium is asymptotically stable, that is no guarantee that the system will reach that equilibrium unless we know that the system's initial state is sufficiently close to the equilibrium. Global stability of an equilibrium, when we have it, gives the equilibrium a much more powerful explanatory role. An equilibrium is globally asymptotically stable if the dynamics carries every possible initial state in the interior of the state space to that equilibrium. If an equilibrium is globally stable, (...) it can have.. (shrink)

We develop several aspects of local and global stability in continuous first order logic. In particular, we study type-definable groups and genericity.

The main goal of this paper is to introduce the notion of stabilizers in \(L\)-algebras and develop stabilizer theory in \(L\)-algebras. In this paper, we introduced the notions of left and right stabilizers and investigated some related properties of them. Then, we discussed the relations among stabilizers, ideal and co-annihilators. Also, we obtained that the set of all ideals of a \(CKL\)-algebra forms a relative pseudo-complemented lattice. In addition, we proved that right stabilizers in \(CKL\)-algebra are ideals. Then by using (...) the right stabilizers we produced a basis for a topology on \(L\)-algebra. We showed that the generated topology by this basis is Baire, connected, locally connected and separable and we investigated the other properties of this topology. (shrink)

Standard adaptive control is the preferred approach for stabilization and synchronization of chaotic systems when the structure of such systems is a priori known but the parameters are unknown. However, in the presence of unmodeled dynamics and/or disturbance, this approach is not effective anymore due to the drift of the parameter estimations, which eventually causes the instability of the closed-loop system. In this paper, a robustifying term, which consists of a saturation function, is used to avoid this problem. The robustifying (...) term is added to the adaptive control law. Consequently, the learning law is also modified. The boundedness of the states and the parameter estimations is rigorously and thoroughly proven by means of Lyapunov like analysis based on Barbalat’s lemma. On these new conditions, the convergence to zero cannot be achieved due to the presence of unmodeled dynamics and/or disturbance. However, it is still possible to guarantee the asymptotic convergence to a bounded zone around zero. The width of this zone can be adjusted by the designer. The performance of this robust approach is verified by numerical simulations. Although, for simplicity, this strategy is only applied to the stabilization and synchronization of Zhang system, the procedure can easily be generalized to a broad class of chaotic systems. (shrink)

In this paper, we study a stability transfer theorem in d-tame metric abstract elementary classes, in a similar way as in 2, but using superstability-like assumptions which involves a new independence notion instead of ℵ0-locality.

This essay touches on a number of topics in philosophy of quantum field theory from the point of view of the LSZ asymptotic approach to scattering theory. First, particle/field duality is seen to be a property of free field theory and not of interacting QFT. Second, it is demonstrated how LSZ side-steps the implications of Haag's theorem. Finally, a recent argument due to Redhead, Malament and Arageorgis against the concept of localized particle states is addressed. Briefly, the argument observes (...) that the Reeh-Schlieder theorem entails that correlations between spacelike separated vacuum expectation values of local field operators are always present, and this, according to the above authors, dictates against the notion of a localized particle state. I claim that this moral is excessive and that a coherent notion of localized particles is given by the LSZ approach. The underlying moral to be drawn from this analysis is that questions concerning the ontology of interacting QFT cannot be appropriately addressed if one restricts oneself to the free theory. (shrink)

This paper addresses the robust stabilization problem for a class of stochastic Markovian jump systems with distributed delays. The systems under consideration involve Brownian motion, Markov chains, distributed delays, and parameter uncertainties. By an appropriate Lyapunov–Krasovskii functional, the novel delay-dependent stabilization criterion for the stochastic Markovian jump systems is derived in terms of linear matrix inequalities. When given linear matrix inequalities are feasible, an explicit expression of the desired state feedback controller is given. The designed controller, based on the obtained (...) criterion, ensures asymptotically stable in the mean square sense of the resulting closed-loop system. The convenience of the design is greatly enhanced due to the existence of an adjustable parameter in the controller. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed theory. (shrink)

The postphenomenological framework of concepts—and especially the version utilized by the founder of this school of thought, Don Ihde—has proven useful for puncturing others’ totalizing or otherwise overgeneralizing claims about technology. However, does this specialization in deflating hype leave this perspective unable to identify the kinds of technological patterns necessary for contributing to activist interventions and political critique? Put differently, the postphenomenological perspective is committed to the study of concrete human-technology relations, and it eschews essentialist and fundamentalizing accounts of technology. (...) Do these commitments render it incapable of providing general assessments of our contemporary technological situation? It is my contention that this perspective can indeed be useful for these kinds of critical projects. To do so, we must go beyond Ihde’s personal tendency to utilize postphenomenology mostly for deflating others’ hype, and explore this perspective’s distinctive potential for identifying ways that technologies can become set within problematic patterns of usage and design. My suggestion is that the postphenomenological notion of “multistability” can play a helpful role in these efforts, especially when combined with a conception of local, rather than totalizing, stabilizations of human-technology relationships. (shrink)

To address the possibility that proliferative disorders may originate from interactions between multiple populations of proliferating and maturing cells, we formulate a model for this process as a set of coupled nonlinear first order partial differential equations. Using recent results for the asymptotic behaviour of the solutions to this model, we demonstrate that there exists a region of coupling coefficients, maturation rates, and proliferation rates that will guarantee the stable coexistence of coupled cellular populations. The analysis shows that increases (...) in the coupling between populations may ultimately lead to a loss of stability. Furthermore, the analysis indicates that increases (decreases) in the maturation and/or proliferation rates above (below) critical levels will lead either to instability in the populations or the destruction of one population and the persistence of the other. (shrink)

In this work, our aim is to investigate the impact of a non-Kolmogorov predator-prey-subsidy model incorporating nonlinear prey refuge and the effect of fear with Holling type II functional response. The model arises from the study of a biological system involving arctic foxes, lemmings, and seal carcasses. The positivity and asymptotically uniform boundedness of the solutions of the system have been derived. Analytically, we have studied the criteria for the feasibility and stability of different equilibrium points. In addition, we (...) have derived sufficient conditions for the existence of local bifurcations of codimension 1. It is also observed that there is some time lag between the time of perceiving predator signals through vocal cues and the reduction of prey’s birth rate. So, we have analyzed the dynamical behaviour of the delayed predator-prey-subsidy model. Numerical computations have been performed using MATLAB to validate all the analytical findings. Numerically, it has been observed that the predator, prey, and subsidy can always exist at a nonzero subsidy input rate. But, at a high subsidy input rate, the prey population cannot persist and the predator population has a huge growth due to the availability of food sources. (shrink)

This paper is expected to introduce a novel memductor-based chaotic system. The local dynamical entities, such as the basic dynamical behavior, the divergence, the stability of equilibrium set, and the Lyapunov exponent, are all investigated analytically and numerically to reveal the dynamic characteristics of the new memductor-based chaotic system as the system parameters and the initial state of memristor change. Subsequently, an active control method is derived to study the synchronous stability of the novel memductor-based chaotic system (...) through making the synchronization error system asymptotically stable at the origin. Further to these, a memductor-based chaotic circuit is designed, realized, and applied to construct a new memductor-based secure communication circuit by employing the basic electronic components and memristor. Furthermore, the design principle of the memductor-based chaotic circuit is thoroughly analyzed and the concept of “the memductor-based chaotic circuit defect quantification index” is proposed for the first time to verify whether the chaotic output is consistent with the mathematical model. A good qualitative agreement is shown between the simulations and the experimental validation results. (shrink)

Assuming the existence of a monster model, tameness, and continuity of nonsplitting in an abstract elementary class (AEC), we extend known superstability results: let $\mu>\operatorname {LS}(\mathbf {K})$ be a regular stability cardinal and let $\chi $ be the local character of $\mu $ -nonsplitting. The following holds: 1.When $\mu $ -nonforking is restricted to $(\mu,\geq \chi )$ -limit models ordered by universal extensions, it enjoys invariance, monotonicity, uniqueness, existence, extension, and continuity. It also has local character $\chi (...) $. This generalizes Vasey’s result [37, Corollary 13.16] which assumed $\mu $ -superstability to obtain same properties but with local character $\aleph _0$.2.There is $\lambda \in [\mu,h(\mu ))$ such that if $\mathbf {K}$ is stable in every cardinal between $\mu $ and $\lambda $, then $\mathbf {K}$ has $\mu $ -symmetry while $\mu $ -nonforking in (1) has symmetry. In this case:(a) $\mathbf {K}$ has the uniqueness of $(\mu,\geq \chi )$ -limit models: if $M_1,M_2$ are both $(\mu,\geq \chi )$ -limit over some $M_0\in K_{\mu }$, then $M_1\cong _{M_0}M_2$ ;(b)any increasing chain of $\mu ^+$ -saturated models of length $\geq \chi $ has a $\mu ^+$ -saturated union. These generalize [31] and remove the symmetry assumption in [10, 38].Under $(<\mu )$ -tameness, the conclusions of (1), (2)(a)(b) are equivalent to $\mathbf {K}$ having the $\chi $ -local character of $\mu $ -nonsplitting.Grossberg and Vasey [18, 38] gave eventual superstability criteria for tame AECs with a monster model. We remove the high cardinal threshold and reduce the cardinal jump between equivalent superstability criteria. We also add two new superstability criteria to the list: a weaker version of solvability and the boundedness of the U-rank. (shrink)

The term ‘food security’ has been used in multiple ways and addresses not only issues around availability and accessibility of foods, but also, among others, the sustainability of livelihoods at the local community level—an issue often seen as a basis for the proliferation of local and alternative food networks. Accordingly, in this paper we attempt to develop a theoretical re-framing that is able to link food security with AFNs in arguing that the understanding of the two notions is (...) dynamics and contingent upon the elements that construct them. We use an assemblage approach to analyze a case of Dunedin, a small-size city in New Zealand, in which the community aims to achieve food security through a local food strategy. Through a series of interviews with a group of food activists and academics, public discussions, and two local food forums, we found that food security was understood and performed in its local context through assembling diverse actors and objectives within the AFN. In conclusion, we offer assemblage thinking as an analytical tool to understand how seemingly precarious local food relations are stabilized and assembled so as to open possibilities of achieving food security. (shrink)

A fuzzy predictive fault-tolerant control scheme is proposed for a wide class of discrete-time nonlinear systems with uncertainties, interval time-varying delays, and partial actuator failures as well as unknown disturbances, in which the main opinions focus on the relevant theory of FPFTC based on Takagi-Sugeno fuzzy model description of these systems. The T-S fuzzy model represents the discrete-time nonlinear system in the form of the discrete uncertain time-varying delay state space, which is firstly constructed by a set of local (...) linear models and the nonlinear membership functions. The novel improved state space model can be further obtained by extending the output tracking error to the constructed model. Then the fuzzy predictive fault-tolerant control law based on this extended model is designed, which can increase more control degrees of freedom. Utilizing Lyapunov-Krasovskill theory, less conservative delay-range-dependent stable conditions in terms of linear matrix inequality constraints are given to ensure the asymptotically robust stability of closed-loop system. Meanwhile, the optimized cost function and H-infinity performance index are introduced to the stable conditions to guarantee the robust performance and antidisturbance capability. The simulation results on the temperature control of a strong nonlinear continuous stirred tank reactor show that the proposed control scheme is feasible and effective. (shrink)

This paper is devoted to introduce a novel fourth-order hyperchaotic system. The hyperchaotic system is constructed by adding a linear feedback control level based on a modified Lorenz-like chaotic circuit with reduced number of amplifiers. The local dynamical entities, such as the basic dynamical behavior, the divergence, the eigenvalue, and the Lyapunov exponents of the new hyperchaotic system, are all investigated analytically and numerically. Then, an active control method is derived to achieve global chaotic synchronization of the novel hyperchaotic (...) system through making the synchronization error system asymptotically stable at the origin based on Lyapunov stability theory. Next, the proposed novel hyperchaotic system is applied to construct another new hyperchaotic system with circuit deformation and design a new hyperchaotic secure communication circuit. Furthermore, the implementation of two novel electronic circuits of the proposed hyperchaotic systems is presented, examined, and realized using physical components. A good qualitative agreement is shown between the simulations and the experimental results around 500 kHz and below 1 MHz. (shrink)

. We study a local version of the order property in several frameworks, with an emphasis on frameworks where the compactness theorem fails: (1) Inside a fixed model, (2) for classes of models where the compactness theorem fails and (3) for the first order case. Appropriate localizations of the order property, the independence property, and the strict order property are introduced. We are able to generalize some of the results that were known in the case of local (...) class='Hi'>stability for the first order theories, and for stability for nonelementary classes (existence of indiscernibles, existence of averages, stability spectrum, equivalence between order and instability). In the first order case, we also prove the local version of Shelah's Trichotomy Theorem. Finally, as an application, we give a new characterization of stable types when the ambient first order theory is simple. (shrink)

In this paper, a discrete-time dynamic duopoly model, with nonlinear demand and cost functions, is established. The properties of existence and local stability of equilibrium points have been verified and analyzed. The stability conditions are also given with the help of the Jury criterion. With changing of the values of parameters, the system shows some new and interesting phenomena in terms to stability and multistability, such as V-shaped stable structures and different shape basins of attraction of (...) coexisting attractors. The eye-shaped structures appear where the period-doubling and period-halving bifurcations occur. Finally, by utilizing critical curves, the changes in the topological structure of basin of attraction and the reason of “holes” formation are analyzed. As a result, the generation of global bifurcation, such as contact bifurcation or final bifurcation, is usually accompanied by the contact of critical curves and boundary. (shrink)

General-elimination harmony articulates Gentzen’s idea that the elimination-rules are justified if they infer from an assertion no more than can already be inferred from the grounds for making it. Dummett described the rules as not only harmonious but stable if the E-rules allow one to infer no more and no less than the I-rules justify. Pfenning and Davies call the rules locally complete if the E-rules are strong enough to allow one to infer the original judgement. A method is given (...) of generating harmonious general-elimination rules from a collection of I-rules. We show that the general-elimination rules satisfy Pfenning and Davies’ test for local completeness, but question whether that is enough to show that they are stable. Alternative conditions for stability are considered, including equivalence between the introduction- and elimination-meanings of a connective, and recovery of the grounds for assertion, finally generalizing the notion of local completeness to capture Dummett’s notion of stability satisfactorily. We show that the general-elimination rules meet the last of these conditions, and so are indeed not only harmonious but also stable. (shrink)

To mitigate the spread of schistosomiasis, a deterministic human-bovine mathematical model of its transmission dynamics accounting for contaminated water reservoirs, including treatment of bovines and humans and mollusciciding is formulated and theoretically analyzed. The disease-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number R0<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0<1$$\end{document}, while global stability of the endemic equilibrium is investigated by constructing a suitable Lyapunov function. To support the analytical results, parameter values from (...) published literature are used for numerical simulations and where applicable, uncertainty analysis on the non-dimensional system parameters is performed using the Latin Hypercube Sampling and Partial Rank Correlation Coefficient techniques. Sensitivity analysis to determine the relative importance of model parameters to disease transmission shows that the environment-related parameters namely, εs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon _s$$\end{document} (snails shedding rate of cercariae), ps\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_s$$\end{document} (probability that cercariae shed by snails survive), c (fraction of the contaminated environment sprayed by molluscicides) and μc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu _c$$\end{document} (mortality rate of cercariae) are the most significant to mitigate the spread of schistosomiasis. Mollusciciding, which directly impacts the contaminated environment as a single control strategy is more effective compared to treatment. However, concurrently applying mollusciciding and treatment will yield a better outcome. (shrink)

Heritability is routinely interpreted causally. Yet, what such an interpretation amounts to is often unclear. Here, I provide a causal interpretation of this concept in terms of range of causal influence, one of several causal dimensions proposed within the interventionist account of causation. An information-theoretic measure of range of causal influence has recently been put forward in the literature. Starting from this formalization and relying upon Woodward’s analysis, I show that an important problem associated with interpreting heritability causally, namely the (...) locality problem, amounts, at least partly, to a low invariance and low stability between the genotype/environment and the phenotype of individuals. In light of this, I plead for a causal interpretation of heritability that takes the notions of Woodward’s invariance and stability into consideration. In doing so, I defuse naive causal interpretations of heritability. (shrink)

We introduce a dynamic model for evolutionary games played on a network where strategy changes are correlated according to degree of influence between players. Unlike the notion of stochastic stability, which assumes mutations are stochastically independent and identically distributed, our framework allows for the possibility that agents correlate their strategies with the strategies of those they trust, or those who have influence over them. We show that the dynamical properties of evolutionary games, where such influence neighborhoods appear, differ dramatically (...) from those where all mutations are stochastically independent, and establish some elementary convergence results relevant for the evolution of social institutions. (shrink)

This paper extends scholarship on multi-stakeholder initiatives (MSIs) in the context of corporate social responsibility in three ways. First, I outline a framework to analyze the strength of couplings between actors participating in MSIs. Characterizing an MSI as consisting of numerous local networks that are embedded in a wider global network, I argue that tighter couplings (within local networks) and looser couplings (between local networks) coexist. Second, I suggest that this coexistence of couplings enables MSIs to generate (...) policy outcomes which address the conditions of a transnational regulatory context. I argue that MSIs’ way of organizing enables them to cope with three challenges: the stability, flexibility, and legitimacy of governance. Reflecting on these challenges, the article identifies a number of problems related to MSIs’ role in transnational governance. Third, I discuss the UN Global Compact as an illustrative case and examine problems and opportunities related to its stability, flexibility, and legitimacy. (shrink)

Exploring the locality stereotype with respect to CEO’s trustworthiness, we find that firms whose CEOs are from more reputable hometowns have a higher likelihood of stock price crashes, indicating the presence of a CEO “Trust Exploitation” effect, i.e. a high-trust identity does not guarantee managerial ethics; to the contrary, it could tempt CEOs to abuse outsiders’ trust, camouflage their misconducts and conceal adverse information more severely. The effect of CEO’s perceived trustworthiness on tail risk of stock price remains robust when (...) controlling for the region-level trust of firm’s headquarters, and in 2SLS regression with an instrumental variable. Further, CEO’s “Trust Exploitation” effect is more prominent among firms with lower disclosure quality, higher capital market pressure and higher CEO incentives. Our findings highlight an unexplored imperfection of individual-level trustworthiness as a reliable substitute for formal monitoring devices in terms of improving stock market stability. (shrink)

We present Saharon Shelah's Stability Spectrum and Homogeneity Spectrum theorems, as well as the equivalence between the order property and instability in the framework of Finite Diagrams. Finite Diagrams is a context which generalizes the first order case. Localized versions of these theorems are presented. Our presentation is based on several papers; the point of view is contemporary and some of the proofs are new. The treatment of local stability in Finite Diagrams is new.

This paper presents the problem of robust and nonfragile stabilization of nonlinear systems described by multivariable Hammerstein models. The objective is focused on the design of a nonfragile feedback controller such that the resulting closed-loop system is globally asymptotically stable with robust H ∞ disturbance attenuation in spite of controller gain variations. First, the parameters of linear and nonlinear blocks characterizing the multivariable Hammerstein model structure are separately estimated by using a subspace identification algorithm. Second, approximate inverse nonlinear functions of (...) polynomial form are proposed to deal with nonbijective invertible nonlinearities. Thereafter, the Takagi–Sugeno model representation is used to decompose the composition of the static nonlinearities and their approximate inverses in series with the linear subspace dynamic submodel into linear fuzzy parts. Besides, sufficient stability conditions for the robust and nonfragile controller synthesis based on quadratic Lyapunov function, H ∞ criterion, and linear matrix inequality approach are provided. Finally, a numerical example based on twin rotor multi-input multi-output system is considered to demonstrate the effectiveness. (shrink)

The neurophysiological evidence from the Miyashita group's experiments on monkeys as well as cognitive experience common to us all suggests that local neuronal spike rate distributions might persist in the absence of their eliciting stimulus. In Hebb's cell-assembly theory, learning dynamics stabilize such self-maintaining reverberations. Quasi-quantitive modeling of the experimental data on internal representations in association-cortex modules identifies the reverberations (delay spike activity) as the internal code (representation). This leads to cognitive and neurophysiological predictions, many following directly from the (...) language used to describe the activity in the experimental delay period, others from the details of how the model captures the properties of the internal representations. (shrink)

We present a mathematical model of a fishery on several sites with a variable price. The model takes into account the evolution during the time of the resource, fish and boat movement between the different sites, fishing effort and price that varies with respect to supply and demand. We suppose that the movements of the boats and resource as well as the variation of the price go on at a fast time scale. We use methods of aggregation of variables in (...) order to reduce the number of variables and we derive a reduced model governing two global variables, respectively the biomass of the resource and the fishing effort of the whole fishery. We look for the existence of equilibria of the aggregated model and perform local stability analysis. Two main cases can occur. The first one corresponds to over-exploitation leading to fish extinction. At extinction, the fishing effort tends to a positive value. The second case corresponds to a durable fishery equilibrium which is globally asymptotically stable. In the later case, we show that there exists a number of fishing sites that optimizes the total catch of the fishery. (shrink)

In this paper, I present two presumed alternative definitions of metavalidity for metainferences: Local and Global. I defend the latter, first, by arguing that it is not too weak with respect to metainference-cases, and that local metavalidity is in fact too strong with respect to types. Second, I show that although regarding metainference-schemas Local metavalidity is always stable, Global metavalidity is also stable when the language satisfies reasonable expressibility criteria.

The properties of disulphide bonds relevant to their roles in stabilizing protein conformation are reviewed. Natural disulphides can stabilize folded conformations substantially, in some cases to much greater extents than would be expected from just entropic effects on the unfolded state. The linkage relationship between conformational stability and disulphide stability is illustrated. Disulphides will not, however, increase protein stability if the disulphides are not maintained in the unfolded state or if instability is caused by processes, such as (...) chemical modification or proteolysis, that are not linked to unfolding, either local or global. This is part of the reason why some recent attempts to increase protein stability by introducing new disulphides have had only modest success. Other reasons appear to be the severe energetic constraints on disulphide bond geometry and, in some cases, unfavourable effects of introducing Cys residues by mutation. (shrink)

Concepts of stability and symmetry in irreversible thermodynamics are developed through the analysis of system energy flows. The excess power function, derived from a local energy conservation equation, is shown to yield necessary and sufficient stability criteria for linear and nonlinear irreversible processes. In the absence of symmetry-destroying external forces, the linear range may be characterized by a set of phenomenological coefficient symmetries relating coupled forces and displacements, velocities, and accelerations, whereas rotational phenomena in nonlinear processes may (...) be characterized by skew-symmetric components of the phenomenological coefficients. A physical interpretation of the nature of the skew-symmetric parts is given and the variational principle of minimum dissipation of energy is related to a stability criterion. (shrink)

The paper deals with pp formulas in the language of reduced special groups, and the question of when the validity of a pp formula on each finite subspace of a space of orderings implies its global validity [18]. A large new class of pp formulas is introduced for which this is always the case, assuming the space of orderings in question has finite stability index. The paper also considers pp formulas of the special type $b\in \Pi _{i=1}^{n}\,D\langle 1,a_{i}\rangle $. (...) Formulas of this type with n = 3 are the simplest sort of pp formula not covered by the result, and are also the source of the recent counterexamples in [9] and [19]. (shrink)

We give a complete and elementary proof of the following upward categoricity theorem: let be a local abstract elementary class with amalgamation and joint embedding, arbitrarily large models, and countable Löwenheim–Skolem number. If is categorical in 1 then is categorical in every uncountable cardinal. In particular, this provides a new proof of the upward part of Morley’s theorem in first order logic without any use of prime models or heavy stability theoretic machinery.

Inventory prediction and management is a key issue in a retail store. There are a number of inventory prediction techniques. However, it is difficult to identify a time series prediction model for inventory forecasting that provides uniformly good results for all the products in a store. This paper uses data from a small retail store to demonstrate the variability of results for different modeling techniques and different products. We demonstrate inadequacy of a generic inventory model. Stability and seasonality analysis (...) of the time series is used to identify groups of products exhibiting similar sales patterns. Different clustering techniques are applied to determine reasonable local groups. With the help of Mean absolute percentage error, the effectiveness of dataset partitioning for better inventory management is demonstrated. Appropriate inventory management strategies are proposed based on the stability and seasonality analysis. (shrink)

Instead of considering »being with« in terms of non-problematic, machine-like places, where reliable entities assemble in stable relationships, STS conjures up a world where the achievement of chancy stabilisations and synchronisations is local. We have to analyse how and where a certain regularity and predictability in the intersection of scientists and their instruments, say, or of human individuals and groups, is produced. The paper reviews models of emergence drawn from the history of cybernetics—the canonical »black box,« homeostats, and cellular (...) automata—to enrich our imagination of the stabilisation process, and discusses the concept of »variety« as a way of clarifying its difficulty, with the antiuniversities of the 1960s and the Occupy movement as examples. Failures of »being with« are expectable. In conclusion, the paper reviews approaches to collective decision-making that reduce variety without imposing a neoliberal hierarchy. (shrink)