Chaos最新文献

How to understand the evolution of cooperation remains a scientific challenge. Individual strategy update rule plays an important role in the evolution of cooperation in a population. Previous works mainly assume that individuals adopt one single update rule during the evolutionary process. Indeed, individuals may adopt a mixed update rule influenced by different preferences such as payoff-driven and conformity-driven factors. It is still unclear how such mixed update rules influence the evolutionary dynamics of cooperation from a theoretical analysis perspective. In this work, in combination with the pairwise comparison rule and the conformity rule, we consider a mixed updating procedure into the evolutionary prisoner's dilemma game. We assume that individuals adopt the conformity rule for strategy updating with a certain probability in a structured population. By means of the pair approximation and mean-field approaches, we obtain the dynamical equations for the fraction of cooperators in the population. We prove that under weak selection, there exists one unique interior equilibrium point, which is stable, in the system. Accordingly, cooperators can survive with defectors under the mixed update rule in the structured population. In addition, we find that the stationary fraction of cooperators increases as the conformity strength increases, but is independent of the benefit parameter. Furthermore, we perform numerical calculations and computer simulations to confirm our theoretical predictions.

Recent progress in experimental techniques, such as single particle tracking, allows one to analyze both nonequilibrium properties and an approach to equilibrium. There are examples showing that processes occurring at finite timescales are distinctly different than their equilibrium counterparts. In this work, we analyze a similar problem of an approach to nonequilibrium. We consider an archetypal model of a nonequilibrium system consisting of a Brownian particle dwelling in a spatially periodic potential and driven by an external time-periodic force. We focus on a diffusion process and monitor its development in time. In the presented parameter regime, the excess kurtosis measuring the Gaussianity of the particle displacement distribution evolves in a non-monotonic way: first, it is negative (platykurtic form), next, it becomes positive (leptokurtic form), and then decays to zero (mesokurtic form). Despite the latter fact, diffusion in the long time limit is Brownian, yet non-Gaussian. Moreover, we discover a correlation between non-Gaussianity of the particle displacement distribution and transient anomalous diffusion behavior emerging for finite timescales.

There is much interest in the phenomenon of rate-induced tipping, where a system changes abruptly when forcings change faster than some critical rate. Here, we demonstrate and analyze rate-induced tipping in the classic "Daisyworld" model. The Daisyworld model considers a hypothetical planet inhabited only by two species of daisies with different reflectivities and is notable because the daisies lead to an emergent "regulation" of the planet's temperature. The model serves as a useful thought experiment regarding the co-evolution of life and the global environment and has been widely used in the teaching of Earth system science. We show that sufficiently fast changes in insolation (i.e., incoming sunlight) can cause life on Daisyworld to go extinct, even if life could in principle survive at any fixed insolation value among those encountered. Mathematically, this occurs due to the fact that the solution of the forced (nonautonomous) system crosses the stable manifold of a saddle point for the frozen (autonomous) system. The new discovery of rate-induced tipping in such a classic, simple, and well-studied model provides further supporting evidence that rate-induced tipping-and indeed, rate-induced collapse-may be common in a wide range of systems.

Typical reservoir networks are based on random connectivity patterns that differ from brain circuits in two important ways. First, traditional reservoir networks lack synaptic plasticity among recurrent units, whereas cortical networks exhibit plasticity across all neuronal types and cortical layers. Second, reservoir networks utilize random Gaussian connectivity, while cortical networks feature a heavy-tailed distribution of synaptic strengths. It is unclear what are the computational advantages of these features for predicting complex time series. In this study, we integrated short-term plasticity (STP) and lognormal connectivity into a novel recurrent neural network (RNN) framework. The model exhibited rich patterns of population activity characterized by slow coordinated fluctuations. Using graph spectral decomposition, we show that weighted networks with lognormal connectivity and STP yield higher complexity than several graph types. When tested on various tasks involving the prediction of complex time series data, the RNN model outperformed a baseline model with random connectivity as well as several other network architectures. Overall, our results underscore the potential of incorporating brain-inspired features such as STP and heavy-tailed connectivity to enhance the robustness and performance of artificial neural networks in complex data prediction and signal processing tasks.

Nonlinear circuits can be tamed to produce similar firing patterns as those detected from biological neurons, and some suitable neural circuits can be obtained to propose reliable neuron models. Capacitor C and inductor L contribute to energy storage while resistors consume energy, and the time constant RC or L/R provides a reference scale for neural responses. The inclusion of memristors introduces memory effects by coupling energy flow with the historical states of the circuit. A nonlinear resistor introduces nonlinearity, enriching the circuit's dynamic characteristics. In this work, a neural circuit is constructed and one branch circuit contains a constant voltage source E. The relation between physical variables is confirmed and a memristive oscillator with an exact energy function is proposed. Furthermore, an equivalent map neuron is derived when a linear transformation is applied to the sampled variables of the oscillator-like neuron. The energy function for the memristive oscillator is calculated following Helmholtz's theorem, and the memristive map is expressed with an energy description. It is found that the energy of the periodic state is higher than that of the chaotic state, which highlights the key role of energy in mode conversion. Noise-induced coherence resonance or stochastic resonance is induced under an external field. The adaptive control mechanism influenced by Hamilton energy is investigated, revealing its impact on neural mode transitions. These findings bridge the gap between physical circuit design and neural modeling, providing theoretical insights into applications in neuromorphic computing, signal processing, and energy-efficient control systems.

This study explored the evolution of nonlinear eigenmodes in coupled optical systems supported by PT-symmetric Rosen-Morse complex potential, in which one channel is with gain and the other is with loss. We assessed that the threshold potential above which PT-symmetry breakdown occurs is enhanced by coupling constant, by examining low- and high-frequency eigenmodes of ground and first excited states. The stability of eigenmodes was verified by stability analysis using Bogoliubov-de-Gennes (BdG) equations and it was established that even though the Rosen-Morse potential-supported system can create eigenmodes, it cannot support stable soliton solutions for any potential values. The investigation was extended using the modified Rosen-Morse potential that is nearly PT-symmetric and deduced the conditions for better-defined thresholds, improved damping of growth of perturbation which destabilizes eigenmodes, and advanced control mechanisms to manage perturbations and potential interactions. Propagation dynamics of the eigenmodes and power switching between channels have been studied and the controlling mechanism has been discussed to use coupled systems as optical regulators to precisely direct light between multiple paths. We have explored the significance of couplers in signal-processing applications because they control the intensity of various frequency modes. Optical couplers can be used to develop devices that let light travel in one direction while restricting it in the other which find applications in optical sensing.

Most studies of collective phenomena in oscillator networks focus on directly coupled systems, as exemplified by the classical Kuramoto model. However, there are a growing number of examples in which oscillators interact indirectly via a common external medium, including bacterial quorum sensing (QS) networks, pedestrians walking on a bridge, and centrally coupled lasers. In this paper, we analyze the effects of stochastic phase resetting on a Kuramoto model with indirect coupling. All the phases are simultaneously reset to their initial values at a random sequence of times generated from a Poisson process. On the other hand, the external environmental state is not reset. We first derive a continuity equation for the population density in the presence of resetting and show how the resulting density equation is itself subject to stochastic resetting. We then use an Ott-Antonsen (OA) Ansatz to reduce the infinite-dimensional system to a four-dimensional piecewise deterministic system with subsystem resetting. The latter is used to explore how synchronization depends on a cell density parameter. (In bacterial QS, this represents the ratio of the population cell volume and the extracellular volume.) At high densities, we recover the OA dynamics of the classical Kuramoto model with global resetting. On the other hand, at low densities, we show how subsystem resetting has a major effect on collective synchronization, ranging from noise-induced transitions to slow/fast dynamics.

In this paper, we study a new generalization of the kinetic equation emerging in run-and-tumble models [see, e.g., Angelani et al., J. Stat. Phys. 191, 129 (2024) for a time-fractional version of the kinetic equation]. We show that this generalization leads to a wide class of generalized fractional kinetic (GFK) and telegraph-type equations that depend on two (or three) parameters. We provide an explicit expression of the solution in the Laplace domain and show that, for a particular choice of the parameters, the fundamental solution of the GFK equation can be interpreted as the probability density function of a stochastic process obtained by a suitable transformation of the inverse of a subordinator. Then, we discuss some particularly interesting cases, such as generalized telegraph models, fractional diffusion equations involving higher order time derivatives, and fractional integral equations.

In developing countries, the informal sector plays a crucial role in employing unskilled labor workforce and contributes significantly to economic growth. Informal sector also facilitates skill acquisition, which enhances workers' employability. This research work presents a dynamical model examining how skilled individuals in the informal sector influence unemployment dynamics. The model considers unemployed persons (both unskilled and skilled) and employed persons as dynamic variables. We analyze the feasibility and stability of all equilibria for the proposed dynamical system. A quantity R0, analogous to the basic reproductive ratio in epidemic models, is derived. We also demonstrate the existence of various bifurcations, including transcritical, saddle-node, Hopf, and Bogdanov-Takens bifurcations. Additionally, we apply a graph-theoretical approach to analyze unemployment patterns and connections within the labor workforce. This provides insights into the structure and dynamics of unemployment networks, complementing the dynamical system's analysis. By combining dynamical system's theory with graph theory, this study provides a comprehensive, multi-dimensional understanding of unemployment dynamics in developing economies characterized by substantial informal sector.

We report the effect of nonlinear bias of the frequency of collective oscillations of sin-coupled phase oscillators subject to individual asymmetric Cauchy noises. The noise asymmetry makes the Ott-Antonsen ansatz inapplicable. We argue that, for all stable non-Gaussian noises, the tail asymmetry is not only possible (in addition to the trivial shift of the distribution median) but also generic in many physical and biophysical setups. For the theoretical description of the effect, we develop a mathematical formalism based on the circular cumulants. The derivation of rigorous asymptotic results can be performed on this basis but seems infeasible in traditional terms of the circular moments (the Kuramoto-Daido order parameters). The effect of the entrainment of individual oscillator frequencies by the global oscillations is also reported in detail. The accuracy of theoretical results based on the low-dimensional circular cumulant reductions is validated with the high-accuracy "exact" solutions calculated with the continued fraction method.