Chaos最新文献

As an emerging nonlinear electronic device, the memristor has become a key element for constructing neuromorphic systems owing to its properties of nonvolatile memory, asymmetry, negative differential resistance (NDR), and tunable synaptic plasticity. This paper develops a discrete Rulkov neuron system driven by a continuous memristor based on a triangularly modulated nonlinear memristor model. The work systematically explores how memristive characteristics regulate complex dynamical behaviors from both the device and system perspectives. At the device level, experiments on current-voltage (i-v) hysteresis loops and analyses of NDR reveal several non-ideal characteristics of the memristor, including memory saturation, symmetry breaking, and locally active regions. At the system level, memristive parameters, asymmetry, and NDR effects are shown to induce complex spatiotemporal structures such as synchronization symmetry breaking, multistability, solitary states, and chimera states. Moreover, the coupling between the memory-saturation gating window and the rate of parameter variation can trigger rate-induced tipping (R-tipping) in the system. Further investigation uncovers quantitative correlations between the geometric features of the memristor's i-v characteristics (loop area, intersection angle, and NDR proportion) and the system's complexity metrics, including the Lyapunov exponent, permutation entropy, and recurrence quantification analysis. These findings elucidate the multilevel modulation mechanisms through which the non-ideal properties of the continuous memristors shape the complex dynamics of discrete neural systems, offering new theoretical insights and engineering guidance for the design of highly robust memristive neuromorphic chips and chaos-based secure communication.

The energy management circuit plays an important role in the performance of vibrational energy harvesters (VEHs). The paper investigates the resonance characteristics and impedance matching of a nonlinear bistable electromagnetic VEH equipped with an L-matching network under Gaussian white noise. For the complex circuit equations containing a rectifier, an improved stochastic averaging method is proposed to solve the system's probability density function, yielding analytical expressions for the output DC voltage and power. It is found that adjusting the parameters of the L-matching network enables resonance between the mechanical and electrical subsystems, with an optimal ratio of electrical to mechanical natural frequencies, where the output DC power is maximized. Furthermore, specific values of coil resistance and load resistance optimize both output power and rectification efficiency. Experimental validation demonstrates that the optimized L-matching network increases the rectified voltage by approximately 1.86 times and the output power by about 3.45 times compared to the case without the network, while maintaining robust performance. The obtained results provide theoretical guidance and experimental support for the co-design of electromechanical coupling and circuit impedance matching in nonlinear VEHs under ambient random excitations.

Cooperation is a fundamental phenomenon in human societies and multi-agent systems, yet it remains challenging to sustain among rational individuals. In realistic evolutionary processes, cooperative behavior is inevitably affected by behavioral variation and random perturbations; a common way to capture these effects is to introduce mutation, which allows strategies to occasionally change independently of payoffs. Previous studies have shown that introducing mutation into well-mixed populations can enhance strategic diversity and thereby promote the emergence of cooperation. However, interactions in real social and biological systems are constrained by spatial and social networks rather than being well-mixed, and such population structure can qualitatively change evolutionary outcomes through network reciprocity. Here, we investigate how mutation shapes the evolution of cooperation in repeated games on structured populations. Our simulations reveal that cooperation is difficult to sustain when mutation is extremely rare, whereas moderate mutation substantially promotes cooperation. We further identify parameter-dependent mutation regimes that maximize cooperation, and show that their locations depend on the payoff parameters and the considered strategy sets. Remarkably, mutation can facilitate the emergence of cooperation even when the benefit-cost ratio is only slightly larger than one. Further simulations demonstrate that this promoting effect persists in Erdős-Rényi random networks with different average degrees, indicating the robustness of our results with respect to variations in network structures.

Understanding the drivers of extinction risk in endangered species requires addressing the interplay of disease, population dynamics, and environmental stochasticity. In this study, we developed a disease-ecological model that integrates Allee effects into susceptible-infected-recovered (SIR) dynamics and stochasticity to explore their combined impact. Using Canine Distemper in African wild dogs as the main system, we introduce the Disease-Stochasticity-Tipping (DST) triangle, a framework capturing vulnerabilities that emerge from interactions among disease resilience, stochasticity, and tipping phenomena. Our analysis shows that these forces rarely act independently; their interplay shapes disease eradication and species extinction. Key findings along the disease resilience-tipping edge, weak Allee strength stabilizes populations at endemic equilibria, allowing population recovery, while strong Allee strength may trigger extinction via homoclinic bifurcation, though sufficient disease resilience can prevent collapse. On the disease resilience-stochasticity edge, strong resilience limits the influence of stochastic effects on disease persistence. Stochasticity-tipping edge illustrates at low noise levels, bistable dynamics allow populations to coexist or become extinct depending on initial population sizes, but higher noise intensity drives a shift toward noise-induced tipping. The DST triangle, thus, provides a robust, novel framework for guiding disease management and conservation efforts under stochasticity and the Allee effect.

Multi-agent reinforcement learning (MARL) has made significant strides in enabling coordinated behaviors among autonomous agents. However, most existing approaches assume that communication is instantaneous, reliable, and has unlimited bandwidth; these conditions are rarely met in real-world deployments. This survey systematically reviews recent advances in robust and efficient communication strategies for MARL under realistic constraints, including message perturbations, transmission delays, and limited bandwidth. Furthermore, because the challenges of low-latency reliability, bandwidth-intensive data sharing, and communication-privacy trade-offs are central to practical MARL systems, we focus on three applications involving cooperative autonomous driving, distributed simultaneous localization and mapping, and federated learning. Finally, we identify key open challenges and future research directions, advocating a unified approach that co-designs communication, learning, and robustness to bridge the gap between theoretical MARL models and practical implementations.

We show that in a drive-response coupling framework extreme events are suppressed in the response system by the dominance of a single driving signal. We validate this approach across three distinct response network topologies, namely, (i) a pair of coupled neurons, (ii) a monolayer network of N coupled neurons, and (iii) a two-layer multiplex network each composed of FitzHugh-Nagumo neuronal units. The response networks inherently exhibit extreme events. Our results demonstrate that influencing just one neuron in the response network with an appropriately tuned driving signal is sufficient to control extreme events across all three configurations. In the two-neuron case, suppression of extreme events occurs due to the breaking of phase-locking between the driving neuron and the targeted response neuron. In the case of monolayer and multiplex networks, suppression of extreme events results from the disruption of protoevent frequency dynamics and a subsequent frequency decoupling of the driven neuron from the rest of the network. We also observe that when the size of the neurons in the response network connected to the drive increases, the onset of control occurs earlier, indicating a scaling advantage of the method.

High-frequency trading (HFT) demands adaptive strategies to navigate volatile markets. Current cutting-edge discrete sub-agent frameworks struggle with rigid market condition allocations, limiting adaptability. We propose a hierarchical framework with an attention-based meta-agent for dynamic sub-agent coordination. By leveraging market embeddings and reinforcement learning, the meta-agent optimally adjusts responsibility weights, enabling adaptive action aggregation across market regimes. Experiments on historical second-level HFT data show that the proposed framework outperforms state-of-the-art baselines, achieving a 42.15% total return and a 4.19 Sharpe ratio. Ablation studies validate the contributions of the dynamic sub-agent assign mechanism and multi-head attention mechanism, highlighting the framework's ability to adapt to market transitions and deliver superior performance.

Resilience broadly describes the ability to withstand perturbations. Measures of system resilience have gathered increasing attention across applied disciplines; yet, existing metrics often lack computational accessibility and generalizability. In this work, we review the literature on resilience measures through the lens of dynamical systems theory and numerical methods. In this context, we reformulate pertinent measures into a general form and introduce a resource-efficient algorithm designed for their parallel numerical estimation. By coupling these measures with a global continuation of attractors, we enable their consistent evaluation along system parameter changes. The resulting framework is modular and easily extendable, allowing for the incorporation of new resilience measures as they arise. We demonstrate the framework on a range of illustrative dynamical systems, revealing key differences in how resilience changes across systems. This approach offers a more global and comprehensive perspective compared to traditional linear stability metrics used in local bifurcation analysis, which can overlook inconspicuous but significant shifts in system resilience. This work opens the door to genuinely novel lines of inquiry, such as the development of new early warning signals for critical transitions or the discovery of universal scaling behaviors. The presented exemplary analyses can serve as blueprints for further system-specific investigations and comparative studies on different measures of resilience. All code and computational tools are provided as an open-source contribution to the DynamicalSystems.jl software library.

Biochemical systems are inherently stochastic, particularly those with small-molecule populations. The spatial distribution of molecules plays a critical role and requires the inclusion of spatial coordinates in their analysis. Stochastic models such as the chemical master equation are commonly used to study these systems. However, analytical solutions are limited to specific cases, and stochastic simulations require significant computational resources. To mitigate these challenges, approximation methods, such as the moment approach, reduce the system to a set of ordinary differential equations, thereby lowering the computational requirements. This study investigates the conditions under which the second-moment approach yields exact results during the dynamic evolution of chemical reaction-diffusion networks. The analysis encompasses second-order or higher-order reactions and Hill functions without relying on higher-order moment estimations or closure approximations. Starting with stationary states, we extended the analysis to a dynamic evolution. An enzymatic process and an antithetic feedback system were examined for purely reactive systems, demonstrating the approach's accuracy in capturing system behavior and quantifying errors. The study was further extended to gene regulatory networks governed by Hill functions, including both purely reactive and reaction-diffusion systems, validating the method in spatially distributed contexts. This framework enables precise characterization of biochemical systems, avoiding information loss typically associated with approximations and allowing for stability analysis under fluctuations. These findings optimize computational strategies while providing insights into intracellular signaling and regulatory processes, paving the way for efficient and accurate stochastic modeling in biochemical systems.

We present spatially localized states in graphene nanoribbons using the simple tight-binding model with nearest neighbor interactions, which correctly describes the electronic properties of graphene close to the Fermi level. By monitoring the time evolution of initially localized wave packets, we identify different final states depending on edge geometry and initial condition. For armchair nanoribbons, we find, both numerically and analytically, flat band states that remain strictly localized across the nanoribbon width instead of spreading in the infinite periodic direction. For zigzag nanoribbons, we find partially flat band states at the Fermi level, which are localized both in the transverse and longitudinal directions, different from the well-known localized edge states that extend along the whole length of the zigzag edge and decay to zero in the transverse direction. The effects of nonlinearity induced by interactions on these states and on wave packet spreading in general are examined within the discrete nonlinear Schrödinger equation model in and out of the self-trapping regime. We also examine the effects of disorder by introducing random on-site energies to find that all wave packets evolve to exponentially localized states, as expected. These localization phenomena with different origin, from edge geometry to nonlinearity and disorder, should affect wave propagation and transport in atomically thin two-dimensional nanostructures and should be observed in honeycomb lattice systems in photonics, cold atoms, and other physical contexts, opening new directions toward the targeted transfer of relevant excitations.