Chaos最新文献

Recent research shows that punctuation patterns in texts exhibit universal features across languages. Analysis of Western classical literature reveals that the distribution of spaces between punctuation marks aligns with a discrete Weibull distribution, typically used in survival analysis. By extending this analysis to Chinese literature represented here by three notable contemporary works, it is shown that Zipf's law applies to Chinese texts similarly to Western texts, where punctuation patterns also improve adherence to the law. Additionally, the distance distribution between punctuation marks in Chinese texts follows the Weibull model, though larger spacing is less frequent than in English translations. Sentence-ending punctuation, representing sentence length, diverges more from this pattern, reflecting greater flexibility in sentence length. This variability supports the formation of complex, multifractal sentence structures, particularly evident in Gao Xingjian's Soul Mountain. These findings demonstrate that both Chinese and Western texts share universal punctuation and word distribution patterns, underscoring their broad applicability across languages.

We analyze the equivalents of the celebrated arcsine laws for Brownian motion undergoing Poissonian resetting. We obtain closed-form formulas for the probability density functions of the corresponding random variables in the cases of the first and second arcsine law. Furthermore, we obtain numerical results for the third law.

Brownian motion in one or more dimensions is extensively used as a stochastic process to model natural and engineering signals, as well as financial data. Most works dealing with multidimensional Brownian motion consider the different dimensions as independent components. In this article, we investigate a model of correlated Brownian motion in R2, where the individual components are not necessarily independent. We explore various statistical properties of the process under consideration, going beyond the conventional analysis of the second moment. Our particular focus lies on investigating the distribution of turning angles. This distribution reveals particularly interesting characteristics for processes with dependent components that are relevant to applications in diverse physical systems. Theoretical considerations are supported by numerical simulations and analysis of two real-world datasets: the financial data of the Dow Jones Industrial Average and the Standard and Poor's 500, and trajectories of polystyrene beads in water. Finally, we show that the model can be readily extended to trajectories with correlations that change over time.

This study proposes an innovative hypergraph model to explore the effects of higher-order interactions on the evolution of cooperative behavior in a hyperbolic scale-free network. By adjusting the heterogeneity coefficient and clustering coefficient of the hyperbolic scale-free network, four distinct network structures with notable differences can be obtained. We then map pairwise and three-way interactions to 2-hyperedges and 3-hyperedges, constructing a hypergraph model with higher-order interactions. Our findings reveal that when the proportion of three-way interactions exceeds a critical threshold, cooperative tendencies exhibit explosive growth, leading to a bistable phenomenon of coexisting cooperation and defection. The system's average degree significantly influences the critical mass of initial cooperators needed to maintain stable cooperative behavior. The network structure shows complex, non-linear effects on cooperation. In low-conditions, increasing heterogeneity acts to suppress the appearance of bistable phenomena, while in high clustering conditions, it acts to promote. Increasing clustering tends to suppress the appearance of bistable phenomena in both low and high heterogeneity conditions. Furthermore, the effects of heterogeneity, clustering, and noise factors on cooperation are non-monotonic, exhibiting inverted U-shaped patterns with critical transition points. These findings provide new theoretical perspectives for understanding diverse cooperation patterns in real-world scenarios and suggest the need for dynamic, context-specific approaches when designing strategies to promote cooperation.

The present work investigates stochastic P-bifurcation phenomena in a Duffing-van der Pol vibro-impact oscillator containing a Bingham model under Gaussian white noise excitation. By employing non-smooth transformations and stochastic averaging techniques, an approximate analytical method is proposed to analyze the stochastic response and bifurcation behavior of nonlinear systems with friction and vibro-impact effects. Using a non-smooth transformation, the stochastically excited vibro-impact oscillator is converted into an approximately equivalent system without velocity discontinuities. Subsequently, the friction term is handled, and stochastic averaging is applied to derive the averaged stochastic Itô equation. The corresponding Fokker-Planck-Kolmogorov equation is then solved to obtain the probability density function of the system's steady-state response. Numerical simulations are conducted to verify the reliability of the proposed method. Based on these results, the critical parameter conditions for stochastic P-bifurcation are derived using singularity theory, considering both the amplitude probability density and the joint probability density of system displacement and velocity. Bifurcation diagrams, extreme value plots, amplitude probability density plots, velocity probability density plots, and joint probability density plots of system displacement and velocity are constructed for different parameter spaces. The findings demonstrate that changes in the viscous damping coefficient of the magnetorheological damper, Coulomb damping force, noise intensity, vibro-impact coefficient, and nonlinear damping coefficient can all induce stochastic P-bifurcations.

Telegraphers' equation perturbed by a uniformly moving external harmonic impact is investigated to uncover information useful for distinguishing properties of the time evolution patterns that describe either memoryless or memory-dependent modeling of transport phenomena. Memory effects are incorporated into telegraphers' equation by smearing the first- and second-order time derivatives so that the memory kernel smearing the second-order time derivative acts as the smeared derivative of the smeared first-order time derivative. Such a generalized telegraphers' equation (abbreviated as GTE) is solved under initial conditions that specify the values of the solutions and their time derivatives taken at the initial time and boundary conditions that require the sought solutions to vanish either at the x space infinity or the (+l)/(-l) boundaries of a compact domain. The question is which solutions would be classified as traveling or standing waves. To answer this, we consider the Doppler effect and investigate how the frequency and velocity of external sources influence the obtained solutions. Using the short-time Fourier transform allows us to advance the problem and shows that infinite domain solutions to the GTEs, provided by a model example involving the Caputo fractional derivatives CDt2α and CDtα with 0<α≤1, exhibit a kind of velocity-dependent Doppler-like frequency shift if 12<α≤1. The effect remains unnoticed if 0<α≤12. This confirms our previous hypothesis that the emergence of wave-like effects in solutions of fractional equations is related to the occurrence of fractional time derivatives of the order greater than 1.

Accurate regulation of calcium release is essential for cellular signaling, with the spatial distribution of ryanodine receptors (RyRs) playing a critical role. In this study, we present a nonlinear spatial network model that simulates RyR spatial organization to investigate calcium release dynamics by integrating RyR behavior, calcium buffering, and calsequestrin (CSQ) regulation. The model successfully reproduces calcium sparks, shedding light on their initiation, duration, and termination mechanisms under clamped calcium conditions. Our simulations demonstrate that RyR clusters act as on-off switches for calcium release, producing short-lived calcium quarks and longer-lasting calcium sparks based on distinct activation patterns. Spark termination is governed by calcium gradients and stochastic RyR dynamics, with CSQ facilitating RyR closure and spark termination. We also uncover the dual role of CSQ as both a calcium buffer and a regulator of RyRs. Elevated CSQ levels prolong calcium release due to buffering effects, while CSQ-RyR interactions induce excessive refractoriness, a phenomenon linked to pathological conditions such as ventricular arrhythmias. Dysregulated CSQ function disrupts the on-off switching behavior of RyRs, impairing calcium release dynamics. These findings provide new insights into RyR-mediated calcium signaling, highlighting CSQ's pivotal role in maintaining calcium homeostasis and its implications for pathological conditions. This work advances the understanding of calcium spark regulation and underscores its significance for cardiomyocyte function.

Populations of coupled oscillators can exhibit a wide range of complex dynamical behavior, from complete synchronization to chimera and chaotic states. We can, thus, expect complex dynamics to arise in networks of such populations. Here, we analyze the dynamics of networks of populations of heterogeneous mean-field coupled Kuramoto-Sakaguchi oscillators and show that the instability that leads to chimera states in a simple two-population model also leads to extensive chaos in large networks of coupled populations. Formally, the system consists of a complex network of oscillator populations whose mesoscopic behavior evolves according to the Ott-Antonsen equations. By considering identical parameters across populations, the system contains a manifold of homogeneous solutions where all populations behave identically. Stability analysis of these homogeneous states provided by the master stability function formalism shows that non-trivial dynamics might emerge on a wide region of the parameter space for arbitrary network topologies. As examples, we first revisit the two-population case and provide a complete bifurcation diagram. Then, we investigate the emergent dynamics in large ring and Erdös-Rényi networks. In both cases, transverse instabilities lead to extensive space-time chaos, i.e., irregular regimes whose complexity scales linearly with the system size. Our work provides a unified analytical framework to understand the emergent dynamics of networks of oscillator populations, from chimera states to robust high-dimensional chaos.

Understanding the dynamics of cooperation in public goods games is critical for enhancing collaborative efforts across various domains, yet existing literature often overlooks the complexities introduced by heterogeneous participants. In order to characterize the heterogeneity of populations, we divide individuals into knowledgeable individuals and ordinary individuals, and the games organized by different focal individuals may have different efficiency. In this study, we introduce feedback evolution games where strategies coevolve with the multiplication factor of the defector. Our results indicate that full cooperation is frequently unfeasible in crowdsourcing contexts, consistent with real-world observations. Moreover, for organizers, the increase in the proportion of knowledgeable individuals carries not only direct costs but also indirect costs that may arise from defectors. Importantly, we highlight that the speed of feedback updates plays a crucial role in fostering group cooperation, with a sufficiently high update speed being essential to overcoming social dilemmas. These insights not only advance our understanding of strategic decision-making in collaborative environments but also provide actionable implications for promoting cooperation in complex social systems.

Stock trend prediction is a significant challenge due to the inherent uncertainty and complexity of stock market time series. In this study, we introduce an innovative dual-branch network model designed to effectively address this challenge. The first branch constructs recurrence plots (RPs) to capture the nonlinear relationships between time points from historical closing price sequences and computes the corresponding recurrence quantifification analysis measures. The second branch integrates transposed transformers to identify subtle interconnections within the multivariate time series derived from stocks. Features extracted from both branches are concatenated and fed into a fully connected layer for binary classification, determining whether the stock price will rise or fall the next day. Our experimental results based on historical data from seven randomly selected stocks demonstrate that our proposed dual-branch model achieves superior accuracy (ACC) and F1-score compared to traditional machine learning and deep learning approaches. These findings underscore the efficacy of combining RPs with deep learning models to enhance stock trend prediction, offering considerable potential for refining decision-making in financial markets and investment strategies.