Chaos最新文献

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.

Higher-order topological features extend conventional graph models by capturing multi-node interactions, enabling more accurate modeling of structural robustness in complex systems. However, understanding the structural influence in complex networks remains challenging, especially when connectivity involves multiple scales and higher-order dependencies. This paper introduces the persistent structural influence indicator, which integrates persistent homology with local geometric perturbation analysis to quantify the node influence by extracting latent higher-order topological features from complex networks. Our model effectively captures multi-scale topological features and localized structural sensitivities, providing orthogonal information to classical centrality measures. Evaluations on both synthetic and real-world networks demonstrate that the proposed model more accurately identifies structurally critical nodes, resulting in accelerated network disintegration, reducing the giant component size to 0.12 after 20% node removal compared to 0.23 for degree-based attacks, and more pronounced reductions in post attack connectivity, improves the correlation with ground-truth spreading dynamics by up to 25.1% compared to baseline methods. Furthermore, the prediction model achieves these results without reliance on domain-specific priors or extensive training, balancing interpretability, computational tractability, and structural fidelity. The proposed metric offers a robust, generalizable framework for influence quantification and structural analysis in complex networked systems.

Infectious diseases pose a significant threat to global health security. Higher-order networks have recently emerged as a powerful framework to capture group-based transmission processes. Conventional studies often assume that transmission probabilities scale with group size; however, such probabilities may in fact remain constant due to intrinsic epidemiological properties. In other words, the apparent variation of transmission probabilities may instead arise from additive effects which may stem from time scale variations for various group sizes based on the existing studies. The group-size based multiscale influence on the dynamics is unclear. To elucidate this mechanism, we propose a multiscale epidemic model on hypergraphs incorporating two- and three-body interactions, where transmission intensities are used to unify heterogeneous temporal scales. Two extreme mechanisms are analyzed: individual and group transmission models. We derive the basic reproduction number R0 and perform bifurcation analysis. Our results reveal that R0 depends on both pairwise and triadic transmission intensities and yields only forward bifurcation in individual transmission, whereas in group transmission R0 depends solely on the latter but exhibits backward bifurcation. Subsequently, Monte Carlo simulations validate the models' rationality and further numerical simulations demonstrate that triadic transmission intensity markedly alters the basic reproduction number, steady states, and region distributions of the solutions. These findings highlight how additive effects of group interactions drive multiscale epidemic dynamics, offering new insights into higher-order mechanisms underlying infectious disease spread.

We investigate the recovery dynamics of healthy cardiac activity after physical exertion using multimodal biosignals recorded with a polycardiograph. Multifractal features derived from the singularity spectrum capture the scale-invariant properties of cardiovascular regulation. Five supervised classification algorithms-Logistic Regression (LogReg), Support Vector Machine with radial basis function kernel, k-Nearest Neighbors, Decision Tree, and Random Forest-were evaluated to distinguish recovery states in a small, imbalanced dataset. Our results show that multifractal analysis, combined with multimodal sensing, yields reliable features for characterizing recovery and points toward nonlinear diagnostic methods for heart conditions.

It is demonstrated that the widely used Lennard-Jones (LJ) potential in the mechanics of cross-linked polymers-and an oscillator based on it-can give rise to several notable phenomena: (i) The emergence of subharmonic and superharmonic oscillations across a broad range of driving force amplitudes; (ii) the presence of exponentially decaying amplitudes in the discrete part of the amplitude spectrum, associated with superharmonic components; (iii) the manifestation of multi-periodic, quasi-periodic, and chaotic regimes, depending on the amplitude of the driving force; (iv) the appearance of Feigenbaum cascades at transition zones between multi-periodic and chaotic behavior; and (v) the formation of strange attractors in the corresponding Poincaré sections, indicative of chaotic dynamics. The analysis is based on solving an autonomous system of three coupled first-order equations using the Adams-Bashforth-Moulton solver, which is well-suited for stiff dynamical systems. These findings offer deeper insight into the vibrational performance of seismic and vibration absorbers constructed from rubber-like materials modelled by LJ potentials.