Chaos最新文献

This paper develops a quantitative framework for comparing spread models motivated by rate-based comparisons commonly used in epidemic, population, and spatial propagation studies. We consider 1-spread models on d-ary trees and define the spread rate as the asymptotic proportion of type occurrences in infinite spread patterns. This notion is further extended to generalized spread rates through input-output type vectors, allowing intergenerational transformations to be systematically described. Using ξ-matrices together with elementary and finite shift equivalence, we derive explicit relations between spread rates of different systems. Central to this comparison is the transition constant, a relational quantity that measures the relative dilation or attenuation of asymptotic spread rates between two spread models whose ξ-matrices are finite shift equivalent. We show that the set of attainable transition constants is dense in [1,∞), revealing a wide spectrum of quantitative rate relationships beyond qualitative equivalence. Finally, the framework is applied to population systems by incorporating a movement function, leading to the notion of distribution rates that capture both population growth and spatial migration.

To enhance the structural complexity of multi-cavity chaotic maps, a new complex exponential chaotic map (CECM) is proposed based on complex exponential functions. Its attractor shape is sensitive to parameters. By integrating the CECM with step functions, a heterogeneous multi-cavity hyperchaotic map (HMCM) is created that generates multiple cavities with unique structures, enhancing system complexity. Dynamical analyses, including attractor phase diagram, Lyapunov exponents, and permutation entropy complexity, verify the hyperchaotic performance across a wide parameter range. The HMCM is implemented on a digital signal processor platform, performing on-chip computations of the bifurcation diagram and Lyapunov exponents. The integrated hardware analysis confirms the physical feasibility, robust chaos, and low-resource usage of the map.

From an evolutionary perspective, the pursuit of individual payoff maximization is a widespread behavioral tendency. However, human decision-making is not solely driven by payoffs. Under conditions of uncertainty, risk aversion, and social pressure, individuals often abandon short-term optimal choices and instead conform to locally prevailing behaviors. Along this line, previous studies have investigated how conformity-driven influences the evolution of cooperation in social dilemmas by shaping network reciprocity. Nevertheless, most of these studies treat conformity as a static individual trait, which limits their ability to capture the fact that individuals in real societies flexibly adjust their conformity tendency in response to changing environments. Motivated by this perspective, we propose an adaptive conformity model and examine its impact on the evolution of cooperation in social dilemmas. In this model, individuals dynamically update their conformity tendency based on comparisons between local and global payoffs, with the updating process further modulated by a satisfaction threshold factor and memory length. Through systematic simulations across multiple types of social dilemmas and network topologies, we find that, compared with static conformity models, the adaptive conformity mechanism significantly expands the parameter region in which cooperation can emerge and persist. Specifically, the satisfaction threshold factor exerts a pronounced nonlinear effect on cooperation, whereas longer memory lengths generally suppress the emergence of cooperation. Importantly, even under more severe social dilemma conditions and highly heterogeneous network structures, the proposed model maintains a robust cooperation-promoting effect. These results suggest that adaptive conformity may provide a viable pathway toward mitigating social dilemmas.

Opinion evolution in social networks represents a complex dynamical process, particularly when accounting for the interplay between expressed and private opinions-a dynamic that captures the tension between social conformity and individual authenticity. In this paper, we examine the evolution of these two opinion types in signed networks using the expressed and private opinion (EPO) model, in which each individual carries distinct expressed and private opinions. By applying the lifting technique to the EPO model, we rigorously address the influence of negative edges, while the path-dependence theory is employed to model transitions between consecutive topics. Through analytical study, we derive sufficient conditions to eliminate discrepancies between expressed and private opinions across a sequence of topics, ensuring convergence to zero consensus, bipartite consensus, or bounded opinion stability. Notably, iterative topic discussions lead to asymptotic alignment between private and expressed opinions, with all trajectories confined within a well-defined range. Furthermore, for structurally unbalanced networks, we establish a sufficient condition guaranteeing bipartite consensus. Numerical simulations validate all theoretical findings.

We introduce Kernel Detrended Fluctuation Analysis (kDFA), a multivariate, nonlinear generalization of detrended fluctuation analysis for quantifying long-range persistence in complex systems. We show that kDFA generalizes the traditional variance-based fluctuation functional by replacing it with a kernel cross-covariance-based measure. This formulation connects the estimator to the Hilbert-Schmidt norm of the covariance operator in the reproducing kernel Hilbert space. This allows persistence to be inferred from linear to strongly nonlinear regimes via kernel learning. We showcase kDFA in synthetic and real experiments. On synthetic data, kDFA accurately retrieves Hurst exponents and generalizes the standard DFA to nonlinear cases. Comparisons of the Lorenz systems (both L63 and L96) against iterated amplitude-adjusted Fourier transform surrogates reveal genuine nonlinear persistence beyond linear autocorrelation. Applied to ecosystems, kDFA uncovers robust, long-term coupling between vegetation activity and its drivers across European vegetation sites, and detects patterns in this coupling relative to the long-term vegetation trend. kDFA, thus, provides a scalable, theory-grounded tool to uncover hidden multivariate memory in natural and engineered systems.

Stochastic differential equations are fundamental for modeling complex dynamic systems subject to random noise. However, learning stochastic dynamics from empirical data remains challenging, particularly under degenerate noise conditions where the diffusion matrix is irreversible. Traditional approaches often suffer from numerical instability and prohibitive computational costs in such scenarios. To address these limitations, we propose three novel algorithms tailored for efficient and stable learning of SDEs with degenerate diffusion. Algorithm I integrates numerical techniques from second-order stochastic differential equation (SDE) solvers into a specialized learning framework, targeting the special case of a two-dimensional degenerate stochastic equation. This approach improves computational efficiency by taking advantage of the properties of the physical system. Algorithm II introduces a novel loss function that combines mean squared error and maximum likelihood estimation, specifically designed for systems with degenerate diffusion matrices, improving robustness by explicitly accounting for noise structure in the optimization process. Algorithm III incorporates a stabilizing auxiliary noise mechanism during training, which mitigates gradient instability without sacrificing convergence guarantees. Extensive numerical experiments demonstrate that the proposed methods significantly outperform conventional maximum likelihood estimation in terms of training stability, faster convergence, and higher accuracy. These advances enable reliable modeling of high-dimensional stochastic systems and offer promising tools for neural network learning tasks requiring robust noise adaptation.

The balance between excitation and inhibition (E-I balance) regulates transitions between asynchronous irregular firing and coherent oscillations in cortical networks; yet, the specific contributions of distinct synaptic timescales remain poorly understood. While excitatory transmission is mediated by both fast α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and slow N-methyl-D-aspartate (NMDA) receptors, most theoretical models lump these into a single effective conductance, obscuring their distinct roles in shaping network dynamics. Here, we investigate this problem using a sparsely connected network of quadratic integrate-and-fire neurons incorporating physiologically realistic AMPA, NMDA, and Gamma-aminobutyric acid (GABA) kinetics. By deriving an exact low-dimensional mean-field reduction, we systematically explore the bifurcation structure of the system. We find that shortening the NMDA decay time can lead to transitions between foci and limit cycles, and abrupt alpha-to-gamma frequency jumps reminiscent of epileptic transitions. Conversely, prolonging NMDA or AMPA decay times stabilizes low-rate asynchronous irregular firing activity through enhanced shunting effects, while GABAergic decay kinetics exert only marginal influence in the thermodynamic limit. Furthermore, increasing external drive suppresses oscillations, shifting the network toward the high-rate asynchronous regime associated with heightened arousal. These results demonstrate that glutamatergic receptor kinetics are critical control parameters for E-I balance, providing a mechanistic framework for understanding how synaptic anomalies drive pathological rhythmopathies, such as epilepsy and providing insights into the maintenance of cognitive states.

We present a comprehensive study of a tumor-immune interaction model with delayed immune activation, combining analytical, numerical, and experimental approaches. A central feature of our formulation is the use of a generalized Hill function for immune activation, where the exponent m introduces tunable cooperativity. This generalization extends beyond conventional Michaelis-Menten or fixed-saturation forms and captures a wider range of nonlinear immune responses. On the analytical side, we derive explicit conditions for transcritical and Hopf bifurcations, clarifying the roles of key biological parameters and the immune response delay in shaping tumor dynamics. Numerically, we investigate the time-series, phase-plane plots, and both single- and two-parameter bifurcation scenarios with respect to the delay and other system parameters that confirmed the observed transitions are in excellent agreement with the analytical predictions. Most importantly, we implement the delayed tumor-immune model in an analog electronic circuit by reformulating the Hill activation function in terms of hyperbolic tangents, enabling direct laboratory exploration of the system. Experimental investigations reveal steady-state and oscillatory behaviors, dependent on time delay, that closely match the numerical simulations, despite the unavoidable real-world effects such as parameter mismatch, noise, and fluctuations. To the best of our knowledge, this is the first realization of a time-delayed tumor-immune model in hardware in the physics laboratory. This provides a novel bridge between mathematical theory, numerical analysis, and experimental validation and opens new directions for probing tumor dormancy, immune oscillations, and relapse under controlled physical conditions.

Motivated by important applications in cognitive processes, we explore the constructive role of noise in systems with sequential dynamics. As a conceptual model, we use the well-known May-Leonard model, which describes the dynamics of three populations under competition. For this model, noise-induced phenomena are studied for three important cases. When three axial saddle equilibria are connected by a homoclinic cycle, random noise stabilizes the frequency of stochastic oscillations. In the case where axial equilibria are stable, random disturbances generate stochastic oscillations in the form of sequential dynamics with a temporary slowdown near these equilibria. In the extended version of the model, taking into account a positive constant influx, we reveal the most susceptible parts of the limit cycles. In the analysis of sequential behavior depending on system parameters, scaling laws are identified and stochastic sensitivity technique is used.

We develop a stochastic framework for anyonic systems in which the exchange phase is promoted from a fixed parameter to a fluctuating quantity. Starting from the Stratonovich stochastic Liouville equation, we perform the Stratonovich-Itô conversion to obtain a Lindblad master equation that ties the dissipator directly to the distorted anyon algebra. This construction produces a statistics-dependent dephasing channel, with rates determined by the eigenstructure of the real-symmetric correlation matrix Ξ. The eigenvectors of Ξ select which collective exchange currents-equivalently, which irreducible representations of the system-are protected from stochastic dephasing, providing a natural mechanism for decoherence-free subspaces and noise-induced exceptional points. The key result of our analysis is the universality of the optimal statistical angle: in the minimal two-site model with balanced gain and loss, the protected mode always minimizes its dephasing at θ⋆=π/2, independent of the specific form of Ξ. This robustness highlights a simple design rule for optimizing coherence in noisy anyonic systems, with direct implications for ultracold atomic realizations and other emerging platforms for fractional statistics.