Chaos最新文献

The Kuramoto model is the simplest case of globally coupled phase oscillators with a purely sinusoidal fundamental-harmonic phase coupling function, whose dynamical properties have been extensively studied. While coupled phase oscillators are derived from weakly interacting limit-cycle oscillators via phase reduction, this procedure does not necessarily yield the Kuramoto model or its higher-order extensions exactly for general limit-cycle oscillators and interaction functions, except in the special case of interacting Stuart-Landau oscillators. In this study, we artificially design optimal pairwise and higher-order interaction functions between limit-cycle oscillators, from which higher-order Kuramoto models can be exactly derived via phase reduction for arbitrary smooth limit-cycle oscillators. We validate the results through numerical simulations of FitzHugh-Nagumo oscillators, demonstrating that the collective synchronization dynamics predicted by the reduced higher-order Kuramoto models are realized. Control of the collective phase of the FitzHugh-Nagumo oscillators based on Ott-Antonsen reduction of the higher-order Kuramoto model is also demonstrated.

In the aftermath of large-scale disasters, the scarcity of resources and the paralysis of infrastructure raise severe challenges to effective post-disaster recovery. Efficient coordination between shelters and victims plays a crucial role in building community resilience, yet the evolution of two-layer behavioral feedback between these two groups through network coupling remains insufficiently understood. Here, this study develops a two-layer network to capture the cross-layer coupling between shelters and victims. The upper layer uses a post-disaster emergency resource redistribution model within the framework of the public goods game, while the lower layer adopts a cooperative evolutionary game to describe internal victim interactions. Monte Carlo simulations on scale-free networks reveal threshold effects of incentives: moderate public goods enhancement and subsidies promote cooperation, whereas excessive incentives induce free-riding. In contrast, credible and well-executed punishment effectively suppresses defection. Targeted punishment of highly connected shelters significantly enhances cooperation under resource constraints. A comparative analysis using a network generated from the actual coordinates of Beijing shelters confirms the model's generality and practical applicability. The findings highlight the importance of calibrated incentives, enforceable sanctions, and structural targeting in fostering robust cooperation across organizational and individual levels in post-disaster environments.

This study investigates the fundamental mechanisms underlying cross-species, multi-strain transmission in ecosystems from the opinion of group opinion dynamics. A multilayer interaction framework is proposed, incorporating signed-weighted social network dynamics to quantify group-level opinions and dynamically adjust key epidemiological parameters in real time. The analysis reveals that (1) infection pressure alters group opinion thresholds via cognitive-behavioral feedback, while the emerging collective consensus reciprocally regulates transmission intensity, forming a closed-loop feedback mechanism. (2) The topology of the opinion network governs epidemic phase transitions, inducing a bistable regime characterized by either low-risk (opinion cohesion) or high-risk (opinion polarization) states. By identifying critical nodes within the signed social graph, the study transforms group opinion intensity into dynamic warning thresholds, enabling targeted ecological interventions.

Accurate modeling of coupled nonlinear phenomena is essential for predicting energy transfer in many physical systems; however, conventional coupled-mode theory often relies on approximations that limit its validity under moderate and strong coupling. In this study, a nonlinear coupled-mode framework is developed that systematically incorporates key nonlinear interactions and counter-propagating wave effects, which are typically neglected in traditional formulations. To illustrate the approach, two nonlinear LC circuits containing Josephson junctions are analyzed. Starting from an exact Hamiltonian description, a reduced-order formulation is derived that retains the essential nonlinear and self-coupling contributions, including rapidly oscillating terms. Comparative analysis demonstrates that the conventional coupled-mode model captures only qualitative trends and exhibits significant phase and amplitude errors outside the weak-coupling regime. In contrast, the proposed reduced-order formulation achieves a close quantitative agreement with the exact Hamiltonian dynamics across the weak-to-strong coupling regimes. These findings clarify the limitations of existing phenomenological models and establish a systematic pathway for constructing accurate reduced-order descriptions of coupled nonlinear systems, with implications for circuit dynamics, photonics, and related areas involving energy transfer in complex media.

We investigate how time dependent modulations of drift wave amplitudes affect particle transport and chaos in a magnetized plasma. Using the Horton model, we apply a sawtooth ramp to a primary wave's amplitude and periodic rectangular kicks to secondary waves, simulating a driven system. Particle transport is quantified by the mean square displacement exponent, α, and chaos by the maximum Lyapunov exponent. Our primary finding is a strong negative correlation between the system's average chaoticity and its transport efficiency. We show that rapid sawtooth ramping (short period τ) produces highly efficient, superdiffusive transport (α>1). In contrast, slower ramping increases the system's chaos but suppresses transport, driving it toward normal diffusion (α→1). This counterintuitive result demonstrates that heightened chaos destroys the coherent, streamer like structures necessary for superdiffusive flights. Our findings indicate that the coherence of the turbulent field, rather than its raw chaoticity, is the key determinant of transport efficiency, offering a new perspective on plasma control.

Difference equations have far-reaching implications across various disciplines, particularly in biology. Recent studies have revealed that discrete biological mathematical systems exhibit intricate and complex dynamic behaviors. This paper investigates the stability and bifurcation dynamics of a discrete predator-prey model with a Holling-II type functional response and a nonlinear Michaelis-Menten type harvesting. We employed the semi-discretization method to derive the discrete system and analyzed the existence and local stability of the fixed points. By employing the center manifold theorem and bifurcation theory, we deduced the transcritical bifurcation conditions at the boundary fixed points E1, E2, and E3, as well as the Neimark-Sacker bifurcation conditions at the positive fixed point E4. Numerical simulation validated the correctness of our theoretical analysis and further elucidated the system's dynamic behaviors, including the transitions in the stability of fixed points and the Neimark-Sacker bifurcation phenomena.

During a pandemic, many people face confusion and struggle to decide the most appropriate action to protect themselves by choosing between health-conscious and health-unconscious strategies. This decision is influenced by two main factors: the spread of infection within the population and the perceived benefits or risks of contracting the infection. To remove this confusion, development of an epidemic model with the dynamics of individuals' decision-making processes to investigate how individuals choose the strategies is important. In this study, we introduce an epidemic model in which susceptible, infected, and recovered individuals are partitioned into health-conscious and health-unconscious subpopulations. Our findings indicate that at Nash equilibrium, individuals in both the health-conscious and health-unconscious groups exhibit the same behavior. Local sensitivity analysis quantifies the contribution of individual parameters to the basic reproduction number, while global sensitivity analysis evaluates parameter influence on the infected classes across the full model space. To provide a comprehensive understanding of the overall social benefit, average social payoff is evaluated in both Nash equilibrium and social optimum. Our results also indicate that the social dilemma intensifies as individual costs, waning immunity, and disease transmission rates increase for both groups.

Recent advances in materials science have significantly enhanced our understanding of metamaterials that are specifically designed with unique structural properties. Unlike traditional metamaterials, which have fixed designs, granular metamaterials and metafluids exhibit fascinating dynamics, driven by particle interactions. We are currently studying the behavior of boiling granular films and have developed a robust mathematical model that uses chaotic granular metamaterials to accurately predict this complex behavior. Moreover, our innovative application of chaotic granular thin films-engineered materials that exhibit several emergent properties-enables us to effectively measure the surface energy per unit area. This capability allows for the precise assessment of the surface energy per unit area of wet granular materials containing steam in their pores, with no more than 2.5% water by mass. These advancements present exciting new opportunities for research and applications in material science and chaos theory, paving the way for future innovation.

Since 2011, rafts of floating Sargassum seaweed have frequently obstructed the coasts of the Intra-Americas Seas. The motion of the rafts is represented by a high-dimensional nonlinear dynamical system. Referred to as the eBOMB model, this builds on the Maxey-Riley equation by incorporating interactions between clumps of Sargassum forming a raft and the effects of Earth's rotation. In practical applications, the motion of the centers of mass of the rafts is what matters; however, the law of motion remains undetermined in closed form, making a strong case for using machine learning to develop a low-dimensional model that enables numerical efficiency and facilitates conceptual understanding. In this exploratory work, we evaluate and contrast Long Short-Term Memory (LSTM) Recurrent Neural Networks (RNNs) and Sparse Identification of Nonlinear Dynamics (SINDy). In both cases, a physics-inspired closure modeling approach is taken rooted in eBOMB. Specifically, the LSTM model learns a mapping from a collection of eBOMB variables to the difference between raft center-of-mass and ocean velocities. The SINDy model's library of candidate functions is suggested by eBOMB variables and includes windowed velocity terms incorporating far-field effects of the carrying flow. Overall, the LSTM and SINDy models perform similarly, both operating better with tightly connected rafts but lose precision in more complex scenarios, such as wind effects and loosely connected rafts. LSTM is more effective with simple designs, utilizing fewer neurons and layers, but lacks interpretability, unlike SINDy, which identifies explicit functional dependencies. Including windowed velocity terms enhances modeling of nonlocal interactions, particularly in data sets with sparsely connected rafts.

In exploring the evolution of social cooperation, reputation mechanisms play a crucial role. To construct a model that more closely reflects reality, this paper proposes a reputation dynamics model based on multidimensional states and designs a dual-channel update rule that combines reputation and payoff. This framework enables players' decisions to no longer depend solely on short-term payoffs but to comprehensively evaluate richer, dynamic social reputation signals. This significantly enhances the competitiveness of cooperators in the public goods game dilemma and provides a possibility for their long-term survival. We find that the effect of the reputation mechanism on cooperative behavior is not a monotonic linear pattern. Although increasing the weight of reputation almost always systematically promotes cooperation, the designed reputation system (defined by the intensity of rewards and punishments and the strictness of social norms) is a double-edged sword. Whether increasing the punishment intensity alone or enhancing the strictness of norms, exceeding a critical point can trigger the negative effect of excessive punishment. That is, a severe punishment originally intended to promote cooperation can, when its intensity is too high, systematically destroy the cooperative order, leading to a "cooperation suppression regime." This paper profoundly clarifies the importance of avoiding excessive punishment and maintaining system resilience in reputation design, providing new insights into the evolution of cooperation in complex social systems.