Chaos最新文献_第2页

Topological biomarkers for seizure state transitions. 癫痫状态转换的拓扑生物标志物。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0326217

Ximena Fernández, Diego Mateos

引用次数: 0

Doubly stochastic inter-assembly coupling via entropic optimal transport in echo-state networks for chaotic flows. 混沌流回声状态网络中熵最优输运的双随机装配间耦合。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0304827

Pradeep Singh, Balasubramanian Raman

{"title":"Doubly stochastic inter-assembly coupling via entropic optimal transport in echo-state networks for chaotic flows.","authors":"Pradeep Singh, Balasubramanian Raman","doi":"10.1063/5.0304827","DOIUrl":"https://doi.org/10.1063/5.0304827","url":null,"abstract":"We propose the Optimal-Transport Gated Echo-State Network (OT-ESN), a two-timescale reservoir that replaces ad hoc inter-module couplings with a principled, mass-conserving transport mechanism on a cortical-sheet geometry. At each step, a slow, exogenous controller computes an entropically regularized optimal-transport plan Π between the previous distribution of column activity (source) and an input-derived \"intent\" over columns (target), using a geometric cost that encodes anatomical or functional proximity. The resulting plan-doubly stochastic up to prescribed marginals-acts as a bounded, geometry-aware mixer that gates inter-column blocks of the reservoir at the next fast update. This one-step delay ensures that Π is absent from the time-t Jacobian, so with a 1-Lipschitz nonlinearity and fixed leak, the echo-state property collapses to a single spectral-norm inequality on pre-scaled intra- and inter-column operators, yielding a uniform contraction certificate. OT-ESN, thus, achieves interpretable, neuromodulation-like routing of assembly activity while preserving the simplicity of readout-only training. Computationally, Sinkhorn iterations on a J×J kernel provide efficient, smooth control, with the regularization parameter spanning diffuse (diffusion-like) to sharp (path-like) transports without jeopardizing stability. Ergo, via optimal transport, OT-ESN enables long, structured memory and geometry-respecting information flow in a provably stable recurrent substrate.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 5","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147811652","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

Controlling neural activity by shunting channel current in a memristive FitzHugh-Nagumo circuit. 记忆性FitzHugh-Nagumo电路中通过分流通道电流控制神经活动。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0321416

Binchi Wang, Jiarong Zhao, Zhao Lei, Jun Ma

{"title":"Controlling neural activity by shunting channel current in a memristive FitzHugh-Nagumo circuit.","authors":"Binchi Wang, Jiarong Zhao, Zhao Lei, Jun Ma","doi":"10.1063/5.0321416","DOIUrl":"https://doi.org/10.1063/5.0321416","url":null,"abstract":"Membrane potential is an observable output, whereas the ion channel pathway governs the internal current partitioning that shapes neural firing modes. Here, we construct a memristive FitzHugh-Nagumo neural circuit in which a tunable diversion branch is connected to the canonical ion channel branch, enabling the regulation of neural firing through the controlled redistribution of channel current. Physical implementation of this strategy is verified by incorporating different electric elements in the sub-branch circuit: (i) a shunting capacitor for differential-type diversion and (ii) a shunting inductor in series with a protective resistor for integral-type diversion. For the two controlled circuits, physical equations and field energy functions are derived, and the corresponding theoretical models and corresponding energy functions are obtained and further checked by the Helmholtz theorem. Numerical analysis shows that capacitive shunting can trigger an abrupt collapse of the inductive energy level in L1 and thereby induce firing-mode transitions, whereas inductive shunting produces markedly weaker modulation over comparable parameter ranges. The model also exhibits noise-induced stochastic resonance, and an adaptive energy-guided regulation law controls the electrical activities effectively. The results suggest that control of firing patterns depends on the physical property of the shunting element and provide a physically interpretable strategy for ion-channel-level regulation in memristive neural circuits.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 5","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147811689","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

Bunching of extreme events on complex network. 复杂网络上极端事件的聚类。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0309280

Sarvesh K Upadhyay, Vimal Kishore, Sanjay Kumar, R E Amritkar

引用次数: 0

Entropic and algebraic transcript-based tools in time series analysis. 时间序列分析中的熵和代数转录工具。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0323611

José M Amigó, Roberto Dale

{"title":"Entropic and algebraic transcript-based tools in time series analysis.","authors":"José M Amigó, Roberto Dale","doi":"10.1063/5.0323611","DOIUrl":"https://doi.org/10.1063/5.0323611","url":null,"abstract":"Algebraic representations of time series are symbolic representations whose symbols belong to a finite group. Precisely, the framework of the present paper is the analysis of coupled time series in algebraic representations and, more generally, group-valued time series. The prototype of an algebraic representation is an ordinal representation, whose symbols are permutations, also called ordinal patterns in the context of time series analysis. In fact, permutations, endowed with function composition, build a group called a symmetric group. A simple way to harness the algebraic structure of the alphabet in such cases is the concept of transcript from one group element to another. Since transcripts involve two group elements, they are very suitable for studying couplings between time series in the same algebraic representation. In this paper, we outline several existing entropic and algebraic transcript-based tools for analyzing coupled time series and systems. In addition to entropy, the entropic tools include divergence, statistical complexity, and mutual information. The algebraic tools comprise order classes and, most recently, the Cayley and Kendall distances. We use the detection of generalized synchronization in a well-studied coupled system to compare the performances of some of those tools. To this end, we also provide an alternative tool called the similarity distance between time series, which is a mean Kendall distance. We found that the novel similarity distance outperforms the other tools tested.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 5","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147811663","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 spatiotemporal cell theory for cooperative pattern formation in reinforcement learning-driven evolutionary games. 强化学习驱动进化博弈中合作模式形成的时空细胞理论。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0332366

Hui-Yu Zhang, Yi-Hao Gu, Nan Yao, Xiao-Long Liang, Zi-Gang Huang, Si-Ping Zhang

{"title":"A spatiotemporal cell theory for cooperative pattern formation in reinforcement learning-driven evolutionary games.","authors":"Hui-Yu Zhang, Yi-Hao Gu, Nan Yao, Xiao-Long Liang, Zi-Gang Huang, Si-Ping Zhang","doi":"10.1063/5.0332366","DOIUrl":"https://doi.org/10.1063/5.0332366","url":null,"abstract":"The emergence and stable evolution of cooperation among self-interested individuals is a central issue spanning evolutionary biology, social dynamics, and artificial intelligence. Conventional imitation-based evolutionary game models, lacking mechanisms for active exploration and experiential accumulation, often trap populations in suboptimal steady states and fail to explain the persistence of complex cooperative patterns. In this study, we construct a multi-agent reinforcement learning framework for the spatial snowdrift game and propose a spatiotemporal cell theory that systematically elucidates the mechanisms underlying cooperation driven by autonomous learning. Our results show that agents accumulating interaction experience via Q-learning achieve cooperation levels significantly surpassing classical replicator dynamics across a broad parameter range, with the system self-organizing into robust collective decision-making structures. From an experiential learning perspective, we reveal an endogenous mechanism of cooperative emergence, demonstrating that efficient cooperation can arise solely from individual exploration and local feedback, without external punishment, reputation mechanisms, or centralized control. The spatiotemporal cell theory provides a unified analytical framework that quantifies the coupling between microscopic learning trajectories and macroscopic pattern evolution. Based on this theory, we derive a contour plot of the fraction of cooperators in the α-γ parameter plane that delineates cooperative stability, breakdown, and frozen defect-line phases, and uncover two distinct evolution pathways: cooperative amplification induced by synchronous exploration and noise accumulation driven by asynchronous exploration. This work deepens the understanding of cooperative evolution and provides theoretical support for designing decentralized adaptive multi-agent systems.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 5","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147811687","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

Machine learning for predicting chaotic systems. 预测混沌系统的机器学习。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0313297

Christof Schötz, Alistair White, Maximilian Gelbrecht, Niklas Boers

{"title":"Machine learning for predicting chaotic systems.","authors":"Christof Schötz, Alistair White, Maximilian Gelbrecht, Niklas Boers","doi":"10.1063/5.0313297","DOIUrl":"https://doi.org/10.1063/5.0313297","url":null,"abstract":"Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive domain knowledge, often leading to a shift toward data-driven methods using machine learning. However, existing research provides inconclusive results on which machine learning methods are best suited for predicting chaotic systems. In this paper, we compare different lightweight and heavyweight machine learning architectures using extensive existing benchmark databases of low-dimensional systems, as well as a newly introduced database that allows for uncertainty quantification in the benchmark results. In addition to the state-of-the-art methods from the literature, we also present new advantageous variants of established methods. Hyperparameter tuning is adjusted based on computational cost, with more tuning allocated to less costly methods. Furthermore, we introduce the cumulative maximum error, a novel metric that combines desirable properties of traditional metrics and is tailored for chaotic systems. Our results show that well-tuned simple methods, as well as untuned baseline methods, often outperform the state-of-the-art deep learning models, but their performance can vary significantly with different experimental setups. These findings highlight the importance of aligning prediction methods with data characteristics and caution against the indiscriminate use of overly complex models.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 5","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147811685","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

Early detection of Hopf bifurcations in a prototypical fluid system via deep learning of unbinarized recurrence plots. 基于非二值化递归图深度学习的原型流体系统Hopf分岔早期检测。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0335558

Jungjin Park, Kang Eun Jeon, Zhijian Yang, Haoming Xu, Jun Hur, Bo Yin, Larry K B Li

{"title":"Early detection of Hopf bifurcations in a prototypical fluid system via deep learning of unbinarized recurrence plots.","authors":"Jungjin Park, Kang Eun Jeon, Zhijian Yang, Haoming Xu, Jun Hur, Bo Yin, Larry K B Li","doi":"10.1063/5.0335558","DOIUrl":"https://doi.org/10.1063/5.0335558","url":null,"abstract":"We explore whether deep learning of unbinarized recurrence plots (RPs) can provide early warning signals for the onset of limit-cycle oscillations. We consider a prototypical fluid system exhibiting either a supercritical or a subcritical Hopf bifurcation. From hot-wire velocity measurements, we reconstruct delay-coordinate trajectories and compute unbinarized RPs whose entries are the pairwise distances between reconstructed state vectors. Rather than operating directly on the raw time series, we use these RPs to train a convolutional neural network (ResNet-18) to regress a capped, normalized proximity-to-onset label, yielding a continuous estimate of the proximity to the Hopf point. Compared with established precursors-including the variance, lag-1 autocorrelation, dominant spectral-peak drift, and generalized Hurst exponent-the proposed framework provides a smoother and more reliable warning signal across different operating conditions, including previously unseen ones, without requiring ad hoc instability thresholds. Saliency analysis indicates that the network relies primarily on the evolving boundaries between regions of high and low recurrence, linking predictive performance to changes in the reconstructed phase-space geometry. These results demonstrate the potential of this model-free generalizable framework for the early detection of Hopf bifurcations in fluid flows and other dynamical systems.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 5","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147833652","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

Data denoising and derivative estimation for data-driven modeling of nonlinear dynamical systems. 非线性动力系统数据驱动建模中的数据去噪与导数估计。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0303199

Jiaqi Yao, Lewis Mitchell, John Maclean, Hemanth Saratchandran

引用次数: 0

The periodic orbits of some classes of three-dimensional hybrid relay systems. 几种三维混合继电器系统的周期轨道。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0319706

Jaume Llibre, Alex C Rezende, Leonardo P Serantola

引用次数: 0