Chaos最新文献

This paper presents a recursive method for identifying extreme and superstable curves in the parameter space of dissipative one-dimensional maps. The method begins by constructing an Archimedean spiral with a constant arc length. Subsequently, it identifies extreme and superstable curves by calculating an observable ψ. The spiral is used to locate a region where ψ changes sign. When this occurs, a bisection method is applied to determine the first point on the desired superstable or extreme curve. Once the initial direction is established, the recursive method identifies subsequent points using an additional bisection method, iterating the process until the stopping conditions are met. The logistic-Gauss map demonstrates each step of the method, as it exhibits a wide variety of periodicity structures in the parameter space, including cyclic extreme and superstable curves, which contribute to the formation of period-adding structures. Examples of extreme and superstable curves obtained by the recursive method are presented. It is important to note that the proposed method is generalizable and can be adapted to any one-dimensional map.

All complex phenomena in complex systems arise from individual interactions, which include pairs and higher-order forms. Research indicates that various physical and mental factors can impact the validity of these interactions, potentially preventing diffusion phenomena. This paper explores the influences of the interaction validity on coupling propagation of information and disease in a two-layer higher-order network. Interaction validity is defined using a threshold function based on the individual activity level. The dynamic evolution equations of the nodes are derived by using the microscopic Markov chain approach, and the transmission threshold of the disease is determined. Extensive numerical simulations on both artificial and real-world networks reveal that higher-order interactions significantly enhance the diffusion of disease and related information. Reducing individual activity levels diminishes interaction validity, thereby restricting disease transmission. Moreover, optimizing disease control can be achieved by increasing public activity in virtual social networks while reducing it in physical contact networks. Strengthening interlayer coupling enhances self-protective measures, thus amplifying the suppression of disease by information.

This research studies the properties of two coupled Hodgkin-Huxley neurons. The influence of coupling strength as well as individual parameters of the neurons (i.e., initial conditions and external current values) have been studied. A Pearson correlation coefficient is used to estimate the synchrony degree between the neurons. It was found that the two neurons can be synchronized fairly easily in different regimes based on the combination of parameters: for some cases, the neurons are synchronous in a self-oscillating regime, but for other combinations, a single-spike regime becomes prevalent. It was also discovered that the synchronization regime can be controlled both by the external current value of each neuron and the coupling strength value. The obtained results can be profitable for future research of complex networks of artificial neurons.

Inter-network combat between hierarchical systems plays an essential role in shaping the landscape of everyone's surroundings, influencing fields such as sports tournaments, business competitions, military conflicts, and trade wars. In response, this study proposes a hierarchical combat game model to analyze the dynamics of leader-follower networks engaged in adversarial interactions. Within this model, leaders are motivated by the collective goals, framing the strategic dilemmas faced by followers, who must balance adherence to leadership strategies against minimizing personal risk. Utilizing the leader-follower game as a theoretical framework, the study investigates the impact of leader characteristics on overall success, measured by the winning percentage (WP). The key findings reveal that increasing the number of leaders consistently enhances WP, with the effect being more pronounced in larger populations. However, higher aspiration level and rationality among leaders may impede their chances of winning the game. Additionally, the analysis uncovers strong correlations between the differences in the number of surviving followers, differences in payoffs, and differences in the proportion of followers adopting the Attack strategy, highlighting critical factors that drive success in combat scenarios. Furthermore, our investigation into follower dynamics reveals that the side making the first sacrifice often wins.

Subharmonic entrainment (SHE) of the breathing solitons, an intriguing resonance phenomenon, arises from frequency locking between the breathing frequency and the cavity repetition frequency. This study investigates the phase-locking characteristics and dynamics of the SHE of breathing temporal cavity solitons. We reveal that the breathing solitons arise from the periodic enhancement and depletion of coherence between solitons and pump light, achieving SHE locking across various periods within the stringent parameter ranges of driving intensity, detuning, and cavity finesse. Furthermore, we summarize the excitation condition of SHE within the phase-locking region, enhancing the understanding of the dynamics of SHE. Our research could provide valuable insights into the generation and regulation of SHE.

A non-autonomous system can undergo a rapid change of state in response to a small or slow change in forcing, due to the presence of nonlinear processes that give rise to critical transitions or tipping points. Such transitions are thought possible in various subsystems (tipping elements) of the Earth's climate system. The Atlantic Meridional Overturning Circulation (AMOC) is considered a particular tipping element where models of varying complexity have shown the potential for bi-stability and tipping. We consider both transient and stochastic forcing of a simple but data-adapted model of the AMOC. We propose and test a geometric early warning signal to predict whether tipping will occur for large transient forcing, based on the dynamics near an edge state. For stochastic forcing, we quantify mean times between noise-induced tipping in the presence of stochastic forcing using an Ordered Line Integral Method of Cameron (2017) to estimate the quasipotential. We calculate minimum action paths between stable states for various scenarios. Finally, we discuss the problem of finding early warnings in the presence of both transient and stochastic forcing.

This study examines the complexities of a discrete-time predator-prey model by integrating the impact of prey refuge, with the goal of providing a more realistic understanding of predator-prey interactions. We explore the existence and stability of fixed points within the model, offering a thorough examination of these critical aspects. Furthermore, we use center manifold and bifurcation theory to thoroughly analyze the presence and direction of period-doubling and Neimark-Sacker bifurcations. We also provide numerical simulations to validate our theoretical findings and demonstrate the intricacy of the model. The findings suggest that the inclusion of prey refuge has a notable stabilizing impact on the predator-prey model, hence enhancing the overall stability and resilience of the ecosystem.

Many dynamical systems exhibit unexpected large amplitude excursions in the chronological progression of a state variable. In the present work, we consider the dynamics associated with the one-dimensional Higgs oscillator, which is realized through gnomonic projection of a harmonic oscillator defined on a spherical space of constant curvature onto a Euclidean plane, which is tangent to the spherical space. While studying the dynamics of such a Higgs oscillator subjected to damping and an external forcing, various bifurcation phenomena, such as symmetry breaking, period doubling, and intermittency crises are encountered. As the driven parameter increases, the route to chaos takes place via intermittency crisis, and we also identify the occurrence of extreme events due to the interior crisis. The study of probability distribution also confirms the occurrence of extreme events. Finally, we train the long short-term memory neural network model with the time-series data to forecast extreme events.

This paper analyzes a generalized chaotic system of differential equations characterized by attractors with bondorbital structures. Both classical and fractional-order cases are examined analytically and numerically, with convergence and stability analyses provided. The numerical findings confirm the presence of bondorbital attractors in the classical system. In contrast, bondorbital attractors also emerge in the fractional model employing the Caputo-Fabrizio operator, albeit with significant perturbations for specific fractional orders. To validate these results, an electric circuit implementation of the fractional-order system using an field-programmable gate array board was conducted, yielding consistent outcomes. This study highlights the potential of fractional calculus, particularly the Caputo-Fabrizio operator, in capturing the memory effects and complex dynamics of chaotic systems. The work bridges theoretical modeling and practical hardware applications, offering valuable insights for modeling complex systems.

We prove that if a non-autonomous system has in a certain sense a fast convergence to equilibrium (faster than any power law behavior), then the time τr(x,y) needed for a typical point x to enter for the first time in a ball B(y,r) centered at y, with small radius r, scales as the local dimension of the equilibrium measure μ at y, i.e., limr→0log⁡τr(x,y)-log⁡r=dμ(y). We then apply the general result to concrete systems of different kinds, showing such a logarithm law for asymptotically autonomous solenoidal maps and mean field coupled expanding maps.