Chaos最新文献_第4页

A Bayesian framework for symmetry inference in chaotic attractors. 混沌吸引子对称性推理的贝叶斯框架。

IF 3.2 2区数学

Chaos Pub Date : 2026-04-01 DOI: 10.1063/5.0312423

Ziad Ghanem, Hyunwoong Chang, Preskella Mrad

{"title":"A Bayesian framework for symmetry inference in chaotic attractors.","authors":"Ziad Ghanem, Hyunwoong Chang, Preskella Mrad","doi":"10.1063/5.0312423","DOIUrl":"https://doi.org/10.1063/5.0312423","url":null,"abstract":"Detecting symmetry from data is a fundamental problem in signal analysis, providing insight into underlying structures and constraints. When data emerge as trajectories of dynamical systems, symmetries encode structural properties of the dynamics that enable model reduction, principled comparison across conditions, and detection of regime changes. While recent optimal transport methods provide practical tools for data-driven symmetry detection in this setting, they rely on deterministic thresholds and lack uncertainty quantification, limiting robustness to noise and ability to resolve hierarchical symmetry structures. We present a Bayesian framework that formulates symmetry detection as probabilistic model selection over a lattice of candidate subgroups, using a Gibbs posterior constructed from Wasserstein distances between observed data and group-transformed copies. We establish three theoretical guarantees: (i) a Bayesian Occam's razor favoring minimal symmetry consistent with data, (ii) conjugation equivariance ensuring frame-independence, and (iii) stability bounds under perturbations for robustness to noise. Posterior inference is performed via Metropolis-Hastings sampling and numerical experiments on equivariant dynamical systems and synthetic point clouds demonstrate accurate symmetry recovery under high noise and small sample sizes. An application to human gait dynamics reveals symmetry degradation induced by mechanical constraints, demonstrating the framework's utility for statistical inference in biomechanical and dynamical systems.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 4","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147589981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Transient times and cycle-rich topology in reservoir computing. 油藏计算中的瞬态时间与富循环拓扑。

IF 3.2 2区数学

Chaos Pub Date : 2026-04-01 DOI: 10.1063/5.0302415

Daniel Estevez-Moya, Misha Chai, Erick Alejandro Madrigal Solis, Ernesto Estevez-Rams, Holger Kantz

{"title":"Transient times and cycle-rich topology in reservoir computing.","authors":"Daniel Estevez-Moya, Misha Chai, Erick Alejandro Madrigal Solis, Ernesto Estevez-Rams, Holger Kantz","doi":"10.1063/5.0302415","DOIUrl":"https://doi.org/10.1063/5.0302415","url":null,"abstract":"Training in reservoir computing (RC) requires using an initial part of the input sequence for the reservoir internal state to synchronize with the driver. The length of this transient, often treated as an empirical washout parameter, is a critical resource: too short and training fails, too long and data are wasted. These synchronization transients are quantified and explain when and why they become prohibitively long. For spectral radius ρ<1 (the largest absolute eigenvalue of the recurrent weight matrix), a closed-form upper bound is derived from the linearized dynamics that captures the dependence on tolerance and typical initial separation. Near and above unity, ensemble experiments reveal heavy-tailed transient-time distributions: most realizations synchronize quickly, yet a non-negligible fraction requires orders of magnitude longer washout. Non-linear saturation under driving shortens transients and can restore the Echo State Property even for ρ>1, with rates controlled by input amplitude and leakage. At zero input, persistence vs silence is dictated by topology: interpreting the recurrent weight matrix A as a directed graph and decomposing it into cycles explains which nodes sustain activity (core), which inherit it downstream (driven), and which die out (quiescent). This structure-dynamics correspondence yields practical design rules: pre-screen reservoirs by monitoring state distances; favor cycle-rich topologies or nodes downstream of cycles; avoid very sparse or very dense regimes at large ρ; and tune input scaling/leakage to exploit saturation. Overall, this turns \"washout\" from a heuristic into a measurable, engineerable property with clear levers for robust, data-efficient RC.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 4","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147590102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Bifurcation, chaos, multistability, and pattern formation of a discrete predator-prey model with Allee effect. 具有Allee效应的离散捕食者-猎物模型的分岔、混沌、多稳定性和模式形成。

IF 3.2 2区数学

Chaos Pub Date : 2026-04-01 DOI: 10.1063/5.0302692

Md Jasim Uddin, Duo Li, Hongyang Che, Jiatong Zhu, Songhao Cai, Xintong Jiang, Xuwei Fan, Mainul Haque

{"title":"Bifurcation, chaos, multistability, and pattern formation of a discrete predator-prey model with Allee effect.","authors":"Md Jasim Uddin, Duo Li, Hongyang Che, Jiatong Zhu, Songhao Cai, Xintong Jiang, Xuwei Fan, Mainul Haque","doi":"10.1063/5.0302692","DOIUrl":"https://doi.org/10.1063/5.0302692","url":null,"abstract":"This study constructs a discrete-time model featuring the Holling type II functional response to investigate how the Allee effect drives the appearance of both periodic and chaotic behaviors. Through rigorous algebraic analysis, it is demonstrated that Neimark-Sacker (NS) bifurcations occur when varying the Allee parameter n and the prey's intrinsic growth rate r within the positive quadrant. By applying the center manifold theorem and core results from bifurcation theory, a solid theoretical framework is established to track these qualitative changes. Extensive numerical simulations validate that the system undergoes a subcritical NS bifurcation as n and r change, marking a shift from stable equilibria into chaotic oscillations with increasing Allee intensity. Moreover, the model reveals the coexistence of periodic attractors of periods 11 and 34 over certain (n,r) pairs, underscoring how initial population levels critically shape long-term outcomes. A parallel analysis contrasts this Holling II formulation with its Holling type I analog. By varying the Allee threshold n, it becomes apparent that the type I system collapses at a lower Allee value than the type II system. This disparity suggests that predation saturation-a hallmark of Holling II-confers greater resilience under strong Allee effects. Finally, a comparative evaluation of both functional responses' advantages and limitations highlights the need for adaptive management strategies to preserve biodiversity and maintain ecological stability.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 4","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147608365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Phase turbulence in population models with diffusion and delay. 具有扩散和延迟的种群模型中的相湍流。

IF 3.2 2区数学

Chaos Pub Date : 2026-04-01 DOI: 10.1063/5.0321068

Michael Bestehorn, Thomas M Michelitsch, Elena V Grigorieva

{"title":"Phase turbulence in population models with diffusion and delay.","authors":"Michael Bestehorn, Thomas M Michelitsch, Elena V Grigorieva","doi":"10.1063/5.0321068","DOIUrl":"https://doi.org/10.1063/5.0321068","url":null,"abstract":"Predator-prey type models are commonly used to describe the dynamic interplay of two interacting species, the predator and the prey. Contrary to earlier studies where delay terms represent the lag between birth and maturity of the particular species, we here analyze a delayed predator-prey interaction. Delayed interaction can be associated with the occurrence of an additional intermediate species, generated from the prey and consumed by the predator. In an epidemiological context, this scenario can be connected with a compartment model, where the susceptible compartment plays the role of the prey, the intermediate compartment corresponds to the latency (incubation) period, and the infected and infectious state is identified with the predator. We consider this setting with and without spatial diffusion. The diffusion corresponds to random motions of the microscopic agents. In the case without diffusion and for a sharp delay time (sojourn time in the intermediate state), a Hopf instability emerges when the delay time exceeds a critical threshold. A weakly nonlinear expansion around this critical point leads to a Hopf normal form allowing to determine a stable long-time limit cycle in an explicit form. Including diffusion into the model, we derive the Ginzburg-Landau normal form, which leads to an approximate phase diffusion equation with stable turbulent phase solutions. We derive analytically the coefficients of the Ginzburg-Landau equation and compute the parameter regions where phase turbulence and weak chaos are expected. As new features, defect mediated patterns such as spirals, but also weakly turbulent structures emerge, resulting from the complex interplay of delay and diffusion. In addition to mathematical biology, our model has various interdisciplinary applications in the kinetics of certain chemical reactions, social science, finance, economy, and others.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 4","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147697849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Entrainment effects and information processing in coupled oscillator models of auditory biomechanics. 听觉生物力学耦合振荡模型中的夹带效应和信息处理。

IF 3.2 2区数学

Chaos Pub Date : 2026-04-01 DOI: 10.1063/5.0293621

Bastian Epp, Mikkel Berrig Rasmussen

{"title":"Entrainment effects and information processing in coupled oscillator models of auditory biomechanics.","authors":"Bastian Epp, Mikkel Berrig Rasmussen","doi":"10.1063/5.0293621","DOIUrl":"https://doi.org/10.1063/5.0293621","url":null,"abstract":"The ability to process sound as a means of gaining information about the environment is shared by many species of animals. The auditory system of many vertebrates contains nonlinear and active elements, hair cells, in the inner ear. These are considered elementary for high sensitivity, high selectivity, and wide dynamic range. However, the implications of the complex interplay between active hair cell function and inner ear mechanics on information processing are not yet fully understood. Here, we use the basic properties of vertebrate ears to develop a numerical approach that captures active and nonlinear elements with the goal of quantifying effects of entrainment on information processing. We show that entrainment and the generation of clusters affect information processing and that inclusion of these phenomena extends the scope of commonly used models of hearing. The results show ubiquitous phenomena that are robust against variation of model parameters. We show that the encoding of information emerges as a global effect in the system rather than locally in individual elements. These findings have implications for our understanding of tonotopy in, e.g., the peripheral auditory system and link active and nonlinear dynamic behavior with information encoding in the inner ear. This will help identify the key principles that underlie hearing in complex acoustical environments with strict physiological restrictions.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 4","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147632365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stochastic resonance in higher-order networks driven by colored noise. 有色噪声驱动的高阶网络随机共振。

IF 3.2 2区数学

Chaos Pub Date : 2026-04-01 DOI: 10.1063/5.0327064

Zhongwen Bi, Dan Zhao, Qi Liu, Jürgen Kurths, Yong Xu

引用次数: 0

Limit cycles in planar discontinuous piecewise linear Hamiltonian systems with three equal sectors. 具有三个等扇区的平面不连续分段线性哈密顿系统的极限环。

IF 3.2 2区数学

Chaos Pub Date : 2026-04-01 DOI: 10.1063/5.0315024

Ali Bakhshalizadeh, Jaume Llibre

引用次数: 0

Detecting deterministic chaos in a high-complexity fire model. 高复杂度火灾模型中的确定性混沌检测。

IF 3.2 2区数学

Chaos Pub Date : 2026-04-01 DOI: 10.1063/5.0306306

Jenna Sjunneson McDanold, Alex Jonko, Kara Yedinak, Rod Linn, Sophie Bonner, Alexander Josephson, Nishant Malik

{"title":"Detecting deterministic chaos in a high-complexity fire model.","authors":"Jenna Sjunneson McDanold, Alex Jonko, Kara Yedinak, Rod Linn, Sophie Bonner, Alexander Josephson, Nishant Malik","doi":"10.1063/5.0306306","DOIUrl":"https://doi.org/10.1063/5.0306306","url":null,"abstract":"Sensitivity to wind behaviors has been observed in marginal fire behavior in the field and using high-complexity fire models. Here we use the coupled atmospheric hydrodynamic-fire behavior model FIRETEC to simulate a marginal fire and develop 2028 one-dimensional time series from the temperature of the solid fuel, the convective heat transfer, the magnitude of the horizontal winds, and the vertical wind velocity on and around the leading edge of the fireline. We test each of these time series for chaotic signals using the Chaos 0-1 test that distinguishes between chaotic and non-chaotic time series. We analyze the spatial relationships with the leading edge by including series built from in front of and behind the leading edge of the fireline. We find that the length of the time step can cause a break in the determinism and, therefore, test the series for stochasticity using permutation entropy. We find the leading edge of the fireline to be highly chaotic and spatially correlated. We discuss some challenges in simplifying the time series for application with existing one-dimensional algorithms and discoveries that will lead to future work.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 4","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147763367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Cyclic periodic synchronization in a ring-star network of piecewise-linear discontinuous maps. 分段线性不连续映射环星网的循环周期同步。

IF 3.2 2区数学

Chaos Pub Date : 2026-04-01 DOI: 10.1063/5.0293912

Vismaya V S, Sishu Shankar Muni, Astero Provata

{"title":"Cyclic periodic synchronization in a ring-star network of piecewise-linear discontinuous maps.","authors":"Vismaya V S, Sishu Shankar Muni, Astero Provata","doi":"10.1063/5.0293912","DOIUrl":"https://doi.org/10.1063/5.0293912","url":null,"abstract":"In this paper, we explored the emergence of cyclic periodic synchronization patterns in networks of coupled piecewise-linear discontinuous (PLD) maps. The maps, characterized by the discontinuities in their dynamics, are capable of generating rich nonlinear behavior, including multistability, sensitivity to initial conditions, and complex bifurcation structures. Notably, this PLD map is a discrete version of the differential Chay neuron model, widely used in computational neuroscience, and can generate a similar bifurcation scenario of the inter-spike interval observed in neural experiments. We first analyzed the individual map dynamics through bifurcation diagrams, Lyapunov exponent spectrum, and border-collision bifurcations. In particular, the system exhibits period-adding structures whose boundaries are defined by border-collision bifurcations, providing a clear route to complex synchronization dynamics. Then, we investigated the behavior of these maps in structured coupled networks, focusing on ring, and hybrid ring-star topologies. In these coupled systems, we observed a wide range of spatiotemporal patterns, including the full synchronized state, unsynchronized state, traveling waves, clustered state, and most importantly, cyclic period-3 synchronization pattern, cyclic period-4 synchronization pattern, and cyclic period-5 synchronization pattern. The emergence and stability of these states are strongly influenced by the coupling strength parameters, εr and εs, which play an important role in governing cluster competition and cluster collision, thereby determining the persistence or breakdown of cyclic periodic synchronization patterns. Regime maps in both the parameter and coupling strength revealed the boundaries of these distinct behaviors and demonstrated how interface width and basin boundary influence pattern transitions.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 4","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147763396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A model of corruption on higher-order networks with long-time quasi-stationary solutions. 具有长时间拟平稳解的高阶网络腐蚀模型。

IF 3.2 2区数学

Chaos Pub Date : 2026-04-01 DOI: 10.1063/5.0323948

Nicola Cinardi, Maria Letizia Bertotti

{"title":"A model of corruption on higher-order networks with long-time quasi-stationary solutions.","authors":"Nicola Cinardi, Maria Letizia Bertotti","doi":"10.1063/5.0323948","DOIUrl":"https://doi.org/10.1063/5.0323948","url":null,"abstract":"Corruption is an old, widespread, and almost always unresolved problem. Different responsible actors propose and put into practice various strategies to counteract it. However, effective measures can only be developed with a clear understanding of the underlying mechanism. Mathematical modeling can help figure out the mechanistic description of the phenomenon, including the role of the agents, their interactions, the global structure, and the properties of the population or society under examination. We propose a general framework aimed at describing and analyzing the dynamics through which corruption spreads. Through a set of differential equations that takes into account the networked nature of any community, our model allows, among others, to study individuals split into any number of classes, representing different propensities toward corruption. We show how, thanks to transition matrices, it is possible to model individuals' tendencies for corrupted behavior. The model also allows us to study the impact of group interactions by considering individuals as part of a higher-order network, namely, a simplicial complex. We show that under different parameter settings, initial conditions, and average degree connectivity, the outputs remain qualitatively unchanged: after a transient phase, the dynamics slows down, and there is a progressive increase in the number of corrupt individuals. We find evidence of long-time quasi-stationary solutions for which the number of corrupt individuals keeps increasing. We give insights on how to detect the ideal time for interventions and on thresholds of initial percentage of nearly incorruptible individuals that guarantee a long-time uncorrupted society.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 4","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147763898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0