We study the handicap principle in terms of the Sir Philip Sidney game. The handicap principle asserts that cost is required to allow for honest signalling in the face of conflicts of interest. We show that the significance of the handicap principle can be challenged from two new directions. Firstly, both the costly signalling equilibrium and certain states of no communication are stable under the replicator dynamics ; however, the latter states are more likely in cases where honest signalling should (...) apply. Secondly, we prove the existence and stability of polymorphisms where players mix between being honest and being deceptive and where signalling costs can be very low. Neither the polymorphisms nor the states of no communication are evolutionarily stable, but they turn out to be more important for standard evolutionary dynamics than the costly signalling equilibrium. (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)

The paper starts by identifying dynamic stabilization as a defining feature of modern societies. This term refers to the fact that such a society requires growth, augmentation and high rates of innovation in order to reproduce its structure and to preserve the socioeconomic and political status quo. The subsequent sections explore the mechanisms and consequences of this mode of social reproduction, proceeding in three steps. First, three key aspects or ‘motors’ of dynamization are identified, namely the mechanisms of appropriation, (...) acceleration and activation. In the second step, we argue that this ‘Triple-A-Mode’ of dynamic stabilization necessarily entails a logic of incessant escalation which eventually threatens to undermine itself, leading to a multifaceted process of destabilization. Unmistakable signs of this can be seen in the current financial, democratic, ecological and psychosocial crises. The third and last part briefly and very preliminarily sketches out the possible contours of a ‘post-growth’ society which could move beyond the current mode of dynamic stabilization. (shrink)

The replicator dynamics and Moran process are the main deterministic and stochastic models of evolutionary game theory. The models are connected by a mean-field relationship—the former describes the expected behavior of the latter. However, there are conditions under which their predictions diverge. I demonstrate that the divergence between their predictions is a function of standard techniques used in their analysis and of differences in the idealizations involved in each. My analysis reveals problems for stochastic stability analysis in a broad (...) class of games, demonstrates a novel domain of agreement between the dynamics, and indicates a broader moral for evolutionary modeling. (shrink)

In this paper, the stabilization problem of nonholonomic chained-form systems is addressed with uncertain constants. In this paper, the active disturbance rejection control is designed to solve this problem. The proposed control strategy combines extended state observer and adaptive sliding mode controller. The control of nonholonomic chained-form systems with dynamic nonlinear uncertain terms and uncertain constants is first discussed in this paper. In comparison with existing methods, the proposed method in this paper has better performance. It is proved that, (...) with the application of the proposed control strategy, semiglobal finite-time stabilization of the systems is achieved. An example is given to illustrate the effectiveness of the proposed method. (shrink)

InStabilizing Dynamics Roy Weintraub provides a history of stability theory from the work of Hicks and Samuelson in the late 1930s to the Gale and Scarf counterexamples in the 1960s. Unlike his earlier work in the history of general equilibrium theory this recent contribution is not an attempt to fit the Walrasian program into the narrow framework of some particular philosophy of natural science. Rather, the theme inStabilizing Dynamicsis broadly social constructivist. Simply put, the constructivist view of science is (...) “that scientific knowledge itself is constructed socially, in communities of scientists: Knowledge is constructed, not found”. (shrink)

Today, economic theory is a mathematical theory, but that was not always the case. Major changes in the ways economists presented their arguments to one another occurred between the late 1930s and the early 1950s; over that period the discipline became mathematized. Professor Weintraub, a noted scholar of the modern history of economic thought, argues that those changes were not merely cosmetic: The mathematical forms of the arguments significantly altered the substance of the arguments. Stabilizing Dynamics is particularly concerned with (...) the ways in which the rich and confusing talk of the 1930s evolved, over a fifteen-year period, into technical analysis of some mathematical structures. The author describes the context for the history of that change, locating it in the broader intellectual currents, and shows how the history of modern economics can be seen as a confluence of several disparate traditions. Historiographically, this book offers one of the first constructivist accounts of modern economic analysis. (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)

The image of a ball rolling along a series of hills and valleys is an effective heuristic by which to communicate stability concepts in ecology. However, the dynamics of this landscape model have little to do with ecological systems. Other landscape representations, however, are possible. These include the particle on an energy landscape, the potential landscape, and the Lyapunov function landscape. I discuss the dynamics that these representations admit, and the application of each to ecological modeling and the analysis (...) and representation of stability. (shrink)

The aim of this study is to present a stability in a two-dimensional dynamical system of endogenous growth with public capital. We assume the simple model of the economic growth, in which both private and public capital can influence on the rate of growth of knowledge. The public capital is rival but non excludable goods, i.e. there is a congestion in use of public capital. The model of growth is formulated as a two-dimensional dynamical system. Using mathematical methods of (...) dynamical systems, we analyze growth paths as well as the stationary states of the system and their stability. (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)

In politics, we often observe stasis when, at first sight, no reason exists for such policy blockades. In contrast., we sometimes see policy change when one would expect blockades resulting from veto points or countervailing majorities. How can we explain these contradictory results concerning policy stability? In order to solve this theoretical puzzle, we develop an agent-based model (ABM). We combine established models of veto player theory (Tsebelis 2002: Ganghof-Bräuninger 2006) with the findings of political sociology and party competition. (...) By aggregating previous party-level findings, we show that dynamic representation (Stimson et. al. 1995) provides an additional mechanism that can explain these macro-level outcomes. Parties behaving responsively to their electorate do not automatically guarantee perfect responsivity on the party system level. Further, if opposition parties also fear punishment by the electorate for government inaction, the opposition behaves more accommodatingly than previous approaches have predicted. (shrink)

We study the dynamics and stability of the economics of crime and punishment game from an evolutionary perspective. Specifically, we model the interaction between agents and controllers as an asymmetric game exploring the dynamics of the classic static model using a replicator dynamics equation, given exogenous levels of monitoring and criminal sanctions. The dynamics show five possible equilibria, from which three are stable. Our results show that a culture of honest agents is never stable; however when the penalty is (...) high enough, the system will neutrally tend to an equilibrium of honest agents and a monitoring firm. By contrast, when the probability of detecting wrongdoing is small, the system, in some cases, will remain in a transient state, in which it is impossible to predict the proportion of honest agents. (shrink)

We address the biological dynamics problem of the persistence of several species in conditions of non-existence of an equilibrium, including an example of stabilization by predation and the very controversial “competitive exclusion”. We give normal forms for various examples of such persistence and comments on the involved topology, which implies the presence of exceptional heteroclinic connections binding equilibria on the boundary.

How individuals tend to evaluate the combination of their own and other’s payoffs—social value orientations—is likely to be a potential target of future moral enhancers. However, the stability of cooperation in human societies has been buttressed by evolved mildly prosocial orientations. If they could be changed, would this destabilize the cooperative structure of society? We simulate a model of moral enhancement in which agents play games with each other and can enhance their orientations based on maximizing personal satisfaction. We (...) find that given the assumption that very low payoffs lead agents to be removed from the population, there is a broadly stable prosocial attractor state. However, the balance between prosociality and individual payoff-maximization is affected by different factors. Agents maximizing their own satisfaction can produce emergent shifts in society that reduce everybody’s satisfaction. Moral enhancement considerations should take the issues of social emergence into account. (shrink)

This book develops a general analysis and synthesis framework for impulsive and hybrid dynamical systems.

I investigate the role of stability in cosmology through two episodes from the recent history of cosmology: Einstein’s static universe and Eddington’s demonstration of its instability, and the flatness problem of the hot big bang model and its claimed solution by inflationary theory. These episodes illustrate differing reactions to instability in cosmological models, both positive ones and negative ones. To provide some context to these reactions, I also situate them in relation to perspectives on stability from dynamical systems (...) theory and its epistemology. This reveals, for example, an insistence on stability as an extreme position in relation to the spectrum of physical systems which exhibit degrees of stability and fragility, one which has a pragmatic rationale, but not any deeper one. (shrink)

Multiple sensory signals from visual, somatosensory and vestibular systems are used for human postural control. To maintain postural stability, the central nervous system keeps the center of mass (CoM) within the base of support. The influence of the stomatognathic motor system on postural control has been established under static conditions, but it has not yet been investigated during dynamic steady-state balance. The purpose of the study was to investigate the effects of controlled stomatognathic motor activity on the control (...) and stability of the CoM during dynamic steady-state balance. A total of 48 physically active and healthy adults were assigned to three groups with different stomatognathic motor conditions: jaw clenching, tongue pressing and habitual stomatognathic behavior. Dynamic steady-state balance was assessed using an oscillating platform and the kinematic data were collected with a 3D motion capturing system. The path length (PL) of the 3D CoM trajectory was used for quantifying CoM sway. Temporal dynamics of the CoM movement was assessed with a detrended fluctuation analysis (DFA). An uncontrolled manifold (UCM) analysis was applied to assess the stability and control of the CoM with a subject-specific anthropometric 3D model. The statistical analysis revealed that the groups did not differ significantly in PL, DFA scaling exponents or UCM parameters. The results indicated that deliberate jaw clenching or tongue pressing did not seem to affect the sway, control or stability of the CoM on an oscillating platform significantly. Because of the task-specificity of balance, further research investigating the effects of stomatognathic motor activities on dynamic steady-state balance with different movement tasks are needed. Additionally, further analysis by use of muscle synergies or co-contractions may reveal effects on the level of muscles, which were not visible on the level of kinematics. This study can contribute to the understanding of postural control mechanisms, particularly in relation to stomatognathic motor activities and under dynamic conditions. (shrink)

Several authors have investigated the question of whether canonical logic-based accounts of belief revision, and especially the theory of AGM revision operators, are compatible with the dynamics of Bayesian conditioning. Here we show that Leitgeb's stability rule for acceptance, which has been offered as a possible solution to the Lottery paradox, allows to bridge AGM revision and Bayesian update: using the stability rule, we prove that AGM revision operators emerge from Bayesian conditioning by an application of the principle (...) of maximum entropy. In situations of information loss, or whenever the agent relies on a qualitative description of her information state - such as a plausibility ranking over hypotheses, or a belief set - the dynamics of AGM belief revision are compatible with Bayesian conditioning; indeed, through the maximum entropy principle, conditioning naturally generated AGM revision operators. This mitigates an impossibility theorem of Lin and Kelly for tracking Bayesian conditioning with AGM revision, and suggests an approach to the compatibility problem that highlights the information loss incurred by acceptance rules in passing from probabilistic to qualitative representations of beliefs. (shrink)

The vestibular system is critical for human locomotion. Any deteriorated vestibular system leads to gait instability. In the past decades, these alternations in gait patterns have been majorly measured by the spatial-temporal gait parameters and respective variabilities. However, measuring gait characteristics cannot capture the full aspect of motor controls. Thus, to further understand the effects of deteriorated vestibular system on gait performance, additional measurement needs to be taken into consideration. This study proposed using the margin of stability to identify (...) the patterns of dynamic control under different types of mastoid vibrations in walking. This study hypothesized that using the MOS method could facilitate the understanding of another aspect of motor control induced by different types of mastoid vibrations, and applying the mastoid vibrations could induce the asymmetric MOS. Twenty healthy young adults were recruited. Two electromechanical vibrotactile transducers were placed on the bilateral mastoid process to apply different types of vestibular vibrations. A motion capture system with eight cameras was used to measure the MOSap, MOSml, and respective variabilities. The results were in line with the hypotheses that both bilateral and unilateral mastoid vibrations significantly increased MOSap, MOSml, and respective variabilities p = 0.001, p < 0.001; p = 0.001, p < 0.01 when compared to the no vibration condition. Also, significantly larger MOSml, MOSml variability, MOSap, and MOSap variability were observed under the unilateral vibration condition than that observed under the bilateral vibration condition. The above-mentioned result found that different types of mastoid vibrations affected the MOS differently, suggesting different patterns of control mechanisms under different sensory-conflicted situations. Besides, a significant difference between the dominant and non-dominant legs was observed in MOSml. Moreover, applying the unilateral mastoid vibrations induced a greater symmetric index of MOSml, suggesting that more active control in balance was needed in the medial-lateral than in the anterior-posterior direction. (shrink)

The high traffic density of railway line causes ballasted track to be extremely busy, and thus it is particularly important to improve the efficiency during railway maintenance. The changing law of dynamic characteristics of ballast bed during operation for the dynamic track stabilizer is conducive to optimize simulation analysis of the vehicle-track system, so as to provide an optimized choice of operating parameters for promoting the pertinence and efficiency of dynamic track stabilizer. This paper presents the acceleration (...) response of vehicle-track-subgrade system during operation of a WD-320 dynamic track stabilizer and proposes the range of effective operating parameters. Then, the influence of operating parameters on the dynamic characteristics of the ballast bed is discussed for searching the optimal operating parameters under the single factor influence. Finally, the change laws including the support stiffness, damping, lateral resistance, and subsidence for the ballast bed are studied, and a parameterized model for dynamic characteristics of the ballast bed which can optimize the selection for operating parameters is constructed, rendering an effective reference variable for improving the simulation accuracy of the vehicle-track coupling system. (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 consider metabolic networks with reversible enzymatic reactions. The model is written as a system of ordinary differential equations, possibly with inputs and outputs. We prove the global stability of the equilibrium , using techniques of monotone systems and compartmental matrices. We show that the equilibrium does not always exist. Finally, we consider a metabolic system coupled with a genetic network, and we study the dependence of the metabolic equilibrium with respect to concentrations of enzymes. We give some conclusions (...) concerning the dynamical behavior of coupled genetic/metabolic systems. (shrink)

In this paper we build a prey–predator model with discrete weight structure for the predator. This model will conserve the number of individuals and the biomass and both growth and reproduction of the predator will depend on the food ingested. Moreover the model allows cannibalism which means that the predator can eat the prey but also other predators. We will focus on a simple version with two weight classes or stage and present some general mathematical results. In the last part, (...) we will assume that the dynamics of the prey is fast compared to the predator’s one to go further in the results and eventually conclude that under some conditions, cannibalism can stabilize the system: more precisely, an unstable equilibrium without cannibalism will become almost globally stable with some cannibalism. Some numerical simulations are done to illustrate this result. (shrink)