Chaos最新文献

This paper innovatively constructs a class of Caputo hetero-order fractional predator-prey systems incorporating cannibalism, fear effect, and double time delays. By differentially setting the fractional orders of prey and predators, the heterogeneous memory effects exhibited by both species during their evolutionary processes are characterized. The model simultaneously integrates the cannibalistic behavior of prey and the fear effect induced by predators, and introduces double time delays (fear effect delay and gestation delay), breaking through the limitation of traditional same-order fractional models in describing the memory differences among species. The research adopts a progressive analysis approach: First, for the non-time-delay system, the uniqueness and boundedness of the system's solutions are proved, the existence conditions of the positive equilibrium point are given, and the local stability criterion is established based on the characteristic equation. Furthermore, with the cannibalism rate and fear parameter as bifurcation parameters, the Hopf bifurcation mechanism is analyzed. Second, for the time-delay system, the focus is on analyzing various combinations of time delays; with time delay as the bifurcation parameter, the stability of the equilibrium point and the conditions for Hopf bifurcation are derived. Finally, the correctness of the theoretical results is verified through multiple sets of numerical simulations.

In voluntary vaccination, adaptive adjustments in government subsidy policies play a crucial role in influencing vaccination levels. The Bush-Mosteller model, a type of reinforcement learning, offers an excellent framework to study the decision-making process of the government. In this work, we study how the government adaptively adjusts to different subsidy policies that affect the vaccination level. Here, we incorporate the per capita treatment cost for infections and the per capita subsidy into a Bush-Mosteller model where the former serves as the payoff and the latter defines the aspiration level, and the gap between the payoff and the aspiration level determines whether the stimulus is positive, resulting in continuation of the current policy, or negative, prompting policy adjustment. Our results reveal that while increasing the total subsidy amount can enhance vaccination levels, reducing the relative vaccination costs fails to increase vaccination levels under a fixed subsidy budget. Provided the total subsidy exactly covers vaccination costs, vaccination levels depend on the dominant strategy: dominance of the partial-offset policy results in a decline, dominance of the free subsidy policy leads to an increase, and the coexistence of both policies maintains the initial level. This study sheds light on the role of adaptive subsidy policies driven by reinforcement learning in shaping vaccination dynamics.

Networked systems-from smart grids and autonomous fleets to social networks-are ubiquitous yet complex, with agents interacting amid topological dependencies and challenges like dynamic environments or malicious attacks. Game theory, control theory, and optimization offer tools to model these systems, but bridging theory with real-world complexity remains a key gap. This Chaos Focus Issue tackles this by exploring intelligent game theory in networked systems, featuring 26 papers across four themes: cooperation promotion, distributed systems, complex structures, and game applications. It links theoretical insights (e.g., cooperative dynamics in structured populations) to practical solutions (e.g., epidemic control, infrastructure protection), advancing resilient, efficient networked system design.

In classical mechanics, driven systems with dissipation often exhibit complex, fractal dynamics known as strange attractors. This paper addresses the fundamental question of how such structures manifest in the quantum realm. We investigate the quantum Duffing oscillator, a paradigmatic chaotic system, using the Caldirola-Kanai framework, where dissipation is integrated directly into a time-dependent Hamiltonian. By employing the Husimi distribution to represent the quantum state in phase space, we present the first visualization of a quantum strange attractor within this model. Our simulations demonstrate how an initially simple Gaussian wave packet is stretched, folded, and sculpted by the interplay of chaotic dynamics and energy loss, causing it to localize onto a structure that beautifully mirrors the classical attractor. This quantum "photograph" is inherently smoothed, blurring the infinitely fine fractal details of its classical counterpart as a direct consequence of the uncertainty principle. We supplement this analysis by examining the out-of-time-ordered correlator, which shows that stronger dissipation clarifies the exponential growth associated with the classical Lyapunov exponent, thereby confirming the model's semiclassical behavior. This work offers a compelling geometric perspective on open chaotic quantum systems and sheds new light on the quantum-classical transition.

We examine theoretically the transparency of electromagnetic pulses through an infinite one-dimensional array of coupled optical microcavities uniformly filled with superconducting qubits-one per cavity. Two types of hybrid matter-light waves, i.e., polaritons and self-induced transparency solitons, govern the transparency of electromagnetic radiation in these media. The spectrum of linear excitations, i.e., polaritons, consists of two branches separated by a relatively wide forbidden band. In the nonlinear regime, the dispersion relation of the carrier wave is determined by soliton width that is controlled by the reciprocal qubit frequency. The separate dispersion curves lie within the polariton forbidden band. Soliton transparency requires that the carrier wave frequency exceeds a threshold value; the latter depends strongly on the pulse width. We find that for pulses with widths ranging from ultrashort to an intermediate limit, the threshold is of the order of the gap frequency value in the photon spectrum. For wider pulses, the threshold frequency gradually decreases to values that are toward the edge of the polariton lower band, provided the soliton width is larger than a critical value. In the overcritical regime, the bandgap appears in the spectrum of the soliton carrier wave, while a twin transparency window appears in the soliton pulse dispersion law. A possible experimental observation of the predicted effects within the proposed setup would be of interest in understanding the properties of self-induced transparency in general and applications in the design of quantum technological devices.

We present a simple and scalable implementation of next-generation reservoir computing (NGRC) for modeling dynamical systems from time-series data. The method uses a pseudorandom nonlinear projection of time-delay embedded inputs, allowing the feature-space dimension to be chosen independently of the observation size and offering a flexible alternative to polynomial-based NGRC projections. We demonstrate the approach on benchmark tasks, including attractor reconstruction and bifurcation diagram estimation, using partial and noisy measurements. We further show that small amounts of measurement noise during training act as an effective regularizer, improving long-term autonomous stability compared to standard regression alone. Across all tests, the models remain stable over long rollouts and generalize beyond the training data. The framework offers explicit control of system state during prediction, and these properties make NGRC a natural candidate for applications such as surrogate modeling and digital-twin applications.

Synchronized rhythmic oscillatory activity in the beta frequency band in the basal ganglia (BG) is a hallmark of Parkinson's disease (PD). Recent experiments and theoretical studies have demonstrated the crucial roles of T-type and L-type calcium currents in shaping the activity patterns of subthalamic nucleus (STN) neurons. However, the role of these currents in the generation of synchronized activity patterns in BG networks involving STN is still unknown. In this study, using an STN model incorporating T-type and L-type calcium currents, we examined how these currents shape the patterns of neural activity in a subthalamo-pallidal network, including network dynamics in response to periodic external inputs. The dynamics were studied in relation to the network connectivity parameters-modulated by dopamine (depleted in PD's BG)-and compared with the properties of the temporal patterning of synchronous neural activity previously observed in the experimental studies with Parkinsonian patients. Stronger T-type current enhanced post-inhibitory rebound bursting and expanded synchronized rhythmic activity, reducing the range of intermittent synchrony and increasing resistance to external entrainment. Stronger L-type current prolonged STN bursts, promoted intermittent synchrony over a wide range of input amplitudes, and sustained beta oscillations, suggesting a potential role in the pathophysiology of PD. These results highlight the interplay between intrinsic cellular properties, synaptic parameters, and external inputs in shaping pathological synchronized rhythms in BG networks. Understanding these network mechanisms may advance the understanding of Parkinsonian rhythmogenesis and further assist in finding ways to modulate and suppress pathological rhythms.

This study investigates the mechanistic effects of vegetation physiological processes and develops a refined vegetation-climate dynamic model with a fractional-in-space diffusion model. The model comprehensively integrates key climatic factors, such as precipitation, temperature, and CO2, to examine the impact of climate change on the evolution of vegetation patterns in the Junggar Basin. Through analysis, we find an inverse relation between the fractional-order coefficient and the size of the Turing instability domain. In addition, performing numerical simulations using real data from the Junggar Basin region, the results show that the interaction between heat stress and the effect of water and CO2 fertilization significantly affect vegetation growth. What is more, the future vegetation growth under different climate scenarios is predicted based on the current scenario and three climate scenarios from the Coupled Model Intercomparison Project Phase 6. We harness the predictive capabilities of machine learning algorithms to forecast changes in the current scenarios. The numerical results show that the current and the SSP1-2.6 scenarios are the favorable climate scenario for vegetation growth. In contrast, the SSP2-4.5 and SSP5-8.5 scenarios suppress vegetation growth and the SSP5-8.5 scenario exhibits the fastest rate of desertification.

Homeostatic adjustment of synaptic weights is important to prevent runaway excitation in neural populations, and it occurs on a slower timescale than the timescale of neural activity. Homeostatic plasticity in neural mass models can induce complex dynamical behaviors, including mixed-mode oscillations (MMOs) and chaos. In this paper, we investigate dynamical mechanisms by studying a single-node Wilson-Cowan model with homeostatic plasticity, which has three timescales associated with the activities of the excitatory/inhibitory (E/I) populations and the homeostatic connection weight, WI, from the I to the E population. We study how the relative timescale separations induce various dynamical behaviors. Analysis in two-timescale settings unveils two typical mechanisms underlying transitions. (1) Considering E as fast and the other variables as slow, canard-induced MMOs due to the presence of a folded node are observed. Bifurcations of folded singularities, including type II folded saddle-node and degenerate folded node, explain the dynamical transitions. (2) Considering WI as slow and E/I as fast, period-doubling cascades and canard explosion, induced by a degenerate folded point, explain the dynamical transitions. Extending to a three-timescale framework introduces interactions between singularities defined in the two-timescale settings and enables a more detailed description of the dynamics. Folded singularities in the three-timescale setting determine the structure of singular orbits. The degenerate folded point in the 2F/1S case determines the transition between MMOs and relaxation oscillation. This paper provides a comprehensive understanding of the role of three timescales in this single-node system and highlights how the connection weights between populations induce complex dynamical behaviors.

Self-organizing network encodes and resembles structural geometry in the heart, offering a new pathway to study cardiac simulation. Hence, we have leveraged the sparsity of an adjacency matrix to design novel simulations of cardiac electrical dynamics on the self-organizing network. However, very little has been done to investigate network simulation of mechanical contraction dynamics. As a vertical step, this paper presents a new self-organizing network methodology for simulation modeling of cardiac contraction dynamics. To this end, we propose to model the self-organizing network as an interconnected spring-mass-damper system and further solve networked dynamic equations to simulate the orchestrated dynamics of mechanical contractions. The proposed methodology is evaluated and illustrated on both 2D cardiac tissues and the 3D heart. Experimental results show that the proposed methodology not only effectively models contraction dynamics in excitable media, but can also be flexibly extended to the whole heart.