Chaos最新文献

Chaotic systems are crucial for security and signal tasks, but many prior systems need higher dimensions or complex nonlinearities, and most give limited validation of fractional-order numerics and security design. This manuscript investigates a new 3D chaotic system containing an absolute-value nonlinearity. The proposed model exhibits no real equilibria and illustrates interesting robust chaotic behaviors affirmed by bifurcation diagrams, Lyapunov exponent, and sensitivity analysis. We generalize the considered new model to the fractional-order system with aid of the Caputo fractional operator. The Haar wavelet method is utilized to derive the numerical results rigorously for the fractional-order system. We portray its dynamical behavior for different fractional orders to show hidden chaotic dynamics. Phase-space portraits affirm the existence of dissipative chaos even at fractional orders ρ<1. A physics-informed symbolic regression framework is implemented to reformulate governing equations from simulated data, attaining high prediction fidelity. On the top of that, the fractional-order system is utilized to gray scale and red-blue-green image encryption. Extensive cryptographic metrics, such as entropy, number of pixels change rate, unified average changing intensity, and correlation coefficients, verify the strength of the algorithm in resisting statistical and differential attacks. The high dimensionality, structural sensitivity, and parameter-tunable complexity of the model make it a powerful tool for uses in secure communication and nonlinear signal processing.

This study explores the use of fractional-order epidemic models to capture the memory-dependent and nonlinear behaviors inherent in cholera transmission. We present a fractional-order susceptible-infected-recovered-individuals adopting preventive measures-bacteria model that integrates preventive behavior and environmental feedback. By applying the Caputo derivative, we demonstrate the existence, uniqueness, and boundedness of the model's solutions and derive an analytical expression for the basic reproduction number R0. Our stability and bifurcation analyses show how memory influences the system's transition from a disease-free to an endemic state via a forward bifurcation. We also design a fractional optimal control strategy that synthesizes health education, protection, and sanitation measures. Numerical simulations indicate that the fractional dynamics help suppress infection peaks by extending transient memory effects, which enhances the system's resilience to epidemics and lowers environmental contamination. These results underscore the profound impact of fractional-order memory and nonlinear coupling on both epidemic thresholds and the effectiveness of control measures, providing new perspectives on the dynamics of waterborne diseases.

Inferring stochastic dynamics from data is central; yet, in many applications, only unordered, non-sequential measurements are available-often restricted to limited regions of state space-so standard time-series methods fail. We introduce DyNoSeD (Identifying Dynamics from Non-Sequential Data), a first-principles framework that identifies unknown dynamical parameters from such non-sequential data by minimizing Fokker-Planck residuals. We develop two complementary routes: a local route that handles region-restricted data via local score estimation, and a global route that fits dynamics from globally sampled data using a kernel Stein discrepancy without density- or score estimation. When the dynamics are affine-in-the-unknown-parameters (while remaining nonlinear-in-the-state), we prove necessary-and-sufficient conditions for the existence and uniqueness of the inferred parameter vector and derive a sensitivity analysis that identifies which parameters are tightly constrained by the data and which remain effectively free under over-parameterization. For general non-affine parameterizations, both routes define differentiable losses amenable to gradient-based optimization. As demonstrations, we recover (i) the three parameters of a stochastic Lorenz system from non-sequential observations (region-restricted data for the local route and full steady-state data for the global route) and (ii) a 3×7 interaction matrix of a nonlinear gene-regulatory network derived from a published B-cell differentiation model, using only unordered steady-state samples and applying the global route. Overall, DyNoSeD provides two first-principles routes for system identification from non-sequential data, grounded in the Fokker-Planck equation, that link data, density, and stochastic dynamics.

Reservoir computing (RC) is a machine learning framework that uses recurrent neural networks and is characterized by directly capitalizing on intrinsic dynamics instead of adjusting internal parameters. In particular, in the form of physical reservoir computing (PRC), recent studies have advanced by treating various physical systems as reservoirs and applying them to time-series data processing and quantifying information-processing properties. In this way, RC and PRC potentially have interdisciplinary impact, and as more researchers from diverse academic disciplines learn and utilize RC and PRC, there is potential for more creative research to emerge. In this paper, we introduce a Jupyter Notebook-based educational material called RC bootcamp for learning RC, being made publicly available under an open-source license (https://rc-bootcamp.github.io/). The RC bootcamp was originally developed and continuously updated within our research group to efficiently train our collaborators and new students, ultimately enabling them to conduct experiments by themselves. Considering the diverse backgrounds of learners, it starts with the basics of computer science and numerical computation using Python/NumPy, as well as fundamental implementations in RC, such as echo state networks and linear regression. Furthermore, it covers important analytical indicators based on dynamical systems theory, such as Lyapunov exponents, echo state property index, and information-processing capacity, as well as cutting-edge approaches utilizing chaos, including first-order, reduced and controlled error (FORCE) learning and innate training, and attractor design via bifurcation embedding. We expect that the RC bootcamp will become a useful educational material for learning RC and PRC and further invigorate research activities in the RC and PRC fields.

This study explores the complexities of Bazikin's type predator-prey model, incorporating the influence of the mate-finding Allee effect on prey population, the impact of cooperative hunting strategies among predators, and the effect of diffusion. It provides a detailed analysis of how these factors influence ecological interactions and affect species dynamics. A detailed theoretical study is carried out to investigate the possible equilibrium states of the temporal model system. This is followed by an analysis of their stability and instability, along with an in-depth analysis of all possible bifurcation scenarios related to various equilibrium points. This model demonstrates saddle-node, Hopf, and Bogdanov-Takens bifurcations about some model parameters. On the other hand, the positivity and boundedness of solutions of the diffusive model are studied. The dynamics of the diffusive model have been investigated, considering linear as well as non-linear analysis. A qualitative analysis using numerical simulations is performed to validate all analytical findings. Numerical simulations demonstrate the development of diffusion-driven patterns, highlighting the emergence of target patterns, chaotic patterns, spots, stripes, and intricate combinations that merge stripes with spots. The simulation outcomes of the diffusive model indicate that multiple factors, including the predator's attack rate, the Allee effect, cooperative hunting behaviors, and diffusion coefficients, shape spatial distributions. The results of the analysis will help us to explore the relevance of various ecological effects and their impact within biology.

Understanding how societies perceive and adapt to environmental change requires analyzing awareness as a dynamic process emerging from coupled human-environment interactions. This study presents a longitudinal, data-driven analysis of environmental awareness based on three years of social-media discourse related to air pollution. Using sentiment analysis (Valence Aware Dictionary and Sentiment Reasoner and Twitter-RoBERTa) and topic modeling (BERTopic), we quantify the temporal evolution of collective public awareness and identify dominant discourse themes. A correlation analysis between sentiment indicators and PM10 levels reveals synchronized fluctuations, while mutual information indicates that public awareness becomes increasingly dependent on or shaped by pollution variability. Furthermore, Kruskal-Wallis tests confirm statistically significant temporal variations in sentiment distributions, underscoring adaptive shifts in public awareness across years. By interpreting awareness as a measurable order parameter within a complex socio-environmental system, this work demonstrates how collective perception emerges from nonlinear feedbacks between environmental forcing and public information flow. The proposed multilayer socio-environmental perception framework integrates machine-learning-based sentiment and topic analysis with complex-systems concepts to quantify emergent awareness dynamics from longitudinal social-media data.

The independent value of the reward and the structural advantages of dynamic networks have been well-established in their respective fields. Yet, research on their integration remains at an exploratory stage. Thus, we effectively incorporated the reward into the dynamic network model to promote cooperation. Numerical simulation results show a clear pattern: When the temptation to defect is low, the cooperation rate stays high regardless of incentive payoff values. However, when the temptation to defect is high, the cooperation rate only remains high if incentive payoff values exceed a certain threshold. These findings demonstrate that the reward can significantly boost cooperation on dynamic networks. The main contributions of this study are threefold: First, to ensure effective integration of the reward into the model, we carefully designed the payoff calculation rule. Second, using the adjusted payoff values, we ingeniously formulated the network-structure evolution rule. Third, through a detailed analysis of the numerical simulation results, we revealed the underlying mechanism behind the improved cooperation levels.

We describe spatiotemporally chaotic (or turbulent) field theories discretized over d-dimensional lattices in terms of sums over their multi-periodic orbits. "Chaos theory" is here recast in the language of statistical mechanics, field theory, and solid-state physics, with the traditional periodic orbits theory of low-dimensional, temporally chaotic dynamics a special, one-dimensional case. In the field-theoretical formulation, there is no time evolution. Instead, treating the temporal and spatial directions on equal footing, one determines the spatiotemporally periodic orbits that contribute to the partition sum of the theory, each a solution of the system's defining deterministic equations, with sums over time-periodic orbits of dynamical systems theory replaced here by sums of d-periodic orbits over d-dimensional spacetime, the weight of each orbit given by the Jacobian of its spatiotemporal orbit Jacobian operator. The weights, evaluated by application of the Bloch theorem to the spectrum of periodic orbit's Jacobian operator, are multiplicative for spacetime orbit repeats, leading to a spatiotemporal zeta-function formulation of the theory in terms of prime orbits.

Congestion and extreme events in transportation networks are emergent phenomena with significant socioeconomic implications. In this work, we study congestion and extreme event properties on nearly-planar real urban street networks drawn from four cities and compare it with that on a regular square grid. For dynamics, we employ three variants of random walk with additional realistic transport features. In all the four urban street networks and 2D square grid and with all dynamical models, phase transitions are observed from a free flow to a congested phase as a function of the birth rate of vehicles. These transitions can be modified by traffic-aware routing protocols, but congestion cannot be entirely mitigated. In street networks without any structure, we observe a weakly congested regime with coexistence of both congested and free-flow components. This regime is suppressed in street networks with a grid-type structure (such as in parts of New York city) and is entirely absent in the regular 2D grid lattice. In the free-flow regime, extreme event occurrence probability is larger for small degree nodes than for hubs. Hence, our results indicate that studying congestion and extreme event properties on synthetic lattices are relevant for real street networks.

In this paper, European freshwater accounts are studied and analyzed to identify how freshwater volumes are distributed around Europe and how they have changed in the past few decades. Specifically, a drought event in the United Kingdom is analyzed, when water abstraction in the 1990s was reduced at a fast pace, changing to a different system state, thus representing a tipping point. Tipping point analysis (its potential forecasting technique) is applied to obtain the hindcast, i.e., forecast in the past, and demonstrates that the hindcast is in agreement with the observed data. Forecasting tipping events, which exemplify nonstationary behavior of a dynamical system, is the most challenging task in time series analysis, and the results demonstrate the promising capability of this technique in forecasting critical transitions.