IF 3.3 2区数学

Chaos Pub Date : 2026-10-01 DOI: 10.1063/5.0335582

Christopher D Marcotte, Matthew J Hoffman, Flavio H Fenton, Elizabeth M Cherry

{"title":"Strongly and weakly coupled data assimilation for reconstruction of three-dimensional synthetic and experimental cardiac electrical excitation states with sparse observations.","authors":"Christopher D Marcotte, Matthew J Hoffman, Flavio H Fenton, Elizabeth M Cherry","doi":"10.1063/5.0335582","DOIUrl":"https://doi.org/10.1063/5.0335582","url":null,"abstract":"Data assimilation practitioners must make design decisions regarding the influence of uncertainties across space, time, and interdependent channels. Using the local ensemble transform Kalman filter, we investigate how different information sharing strategies, namely, strong and weak coupling, affect our ability to reconstruct electrical activity in the heart from sparse observations of state. These two coupling approaches differ in whether observations of one variable are allowed to influence others during the update step. We analyze the potential of a single observation to affect the ensemble weights and span through the spectral properties of the analysis operators. We apply weak and strong coupling in assimilations of observations generated from a numerical model of scroll-wave turbulence and find that restricting information flow from the observations across variable fields (weak coupling) in the low-model error case is effective at improving reconstruction accuracy and robustness. Weak coupling is relatively detrimental for high-model-error reconstructions, and strong coupling produces more reliable estimates of the state. We also consider a case where observations are derived from paced cardiac tissue where only surface voltage is recorded and find in that scenario that while both coupling methods achieve similar degrees of accuracy, strong coupling more closely approximates fine details in the observations, whereas weak coupling provides greater robustness. We conclude that coupling has marginal influence on reconstruction accuracy for cardiac electrical excitation except in extreme cases, i.e., where high-model error precludes accurate reconstruction.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 10","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149179711","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

Ordinal-pattern transition networks as a symbolic substrate for reservoir computing. 有序模式转换网络作为油藏计算的符号基础。

IF 3.3 2区数学

Chaos Pub Date : 2026-10-01 DOI: 10.1063/5.0355934

Max Potratzki, Thomas G de Jong, Michael Small, Timo Bröhl

{"title":"Ordinal-pattern transition networks as a symbolic substrate for reservoir computing.","authors":"Max Potratzki, Thomas G de Jong, Michael Small, Timo Bröhl","doi":"10.1063/5.0355934","DOIUrl":"https://doi.org/10.1063/5.0355934","url":null,"abstract":"Reservoir computing has established itself as a computationally efficient alternative to fully trained recurrent neural networks using a fixed high-dimensional nonlinear substrate to map temporal input into a feature space for a simple readout. Here, we argue that reservoir computing can be realized entirely within a coarse-grained, symbolic state space, and that constrained random walks on ordinal-pattern transition networks provide a natural instance of this realization, replacing the reservoir's continuous state space with a discrete and directly data-derived one. We develop a formal correspondence between the two frameworks, show that the echo-state property has a natural discrete analog in the ergodicity and spectral gap of the walk's underlying Markov chain, and illustrate the correspondence with a minimal example and an empirical one-step-ahead prediction task evaluated across five paradigmatic model systems. These systems exhibit dynamics that correspond to strictly periodic, quasiperiodic, chaotic, or stochastic signals. We argue that this symbolic reservoir perspective allows a redefinition of the reservoir substrate itself, replacing the requirement of a continuous, randomly generated dynamical system with any sufficiently ergodic, data-derived symbolic process. This opens a route toward interpretable, data-adaptive reservoirs whose internal structure is inferred rather than randomly assigned, with implications for surrogate-data methods and reservoir design more broadly.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 10","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149191625","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

Dictionary learning for kernel EDMD. 内核EDMD的字典学习。

IF 3.3 2区数学

Chaos Pub Date : 2026-10-01 DOI: 10.1063/5.0341144

Erik Lien Bolager, Boumediene Hamzi, Houman Owhadi, Ioannis G Kevrekidis, Felix Dietrich

{"title":"Dictionary learning for kernel EDMD.","authors":"Erik Lien Bolager, Boumediene Hamzi, Houman Owhadi, Ioannis G Kevrekidis, Felix Dietrich","doi":"10.1063/5.0341144","DOIUrl":"https://doi.org/10.1063/5.0341144","url":null,"abstract":"Studying nonlinear dynamical systems through their state space behavior can be challenging, and one possible alternative is to analyze them via their associated Koopman operator. This turns the nonlinear problem into a linear, infinite-dimensional one. To approximate the operator in finite dimensions, extended dynamic mode decomposition (EDMD) is a commonly used algorithm. It requires a finite list of functionals and a set of snapshots from the system to compute an approximation of the operator and its corresponding spectrum. Instead of choosing the list of functionals directly, it can be implicitly defined via kernels, a method known as kernel extended dynamic mode decomposition (kEDMD). However, one still needs to define the kernel and choose its parameter values. In this paper, we aim to streamline this process by extending dictionary learning for EDMD to kernel learning in kEDMD. By simplifying kEDMD, we show how to perform gradient-based optimization over the learnable kernel parameters and demonstrate that this method leads to useful kernels for the original kEDMD. The focus of our work is a method that takes a weighted list of kernels with randomly initialized values as input and outputs a list of kernels and parameter values suitable for approximating the Koopman operator of the underlying system. We demonstrate that unimportant kernels can be removed from the list by analyzing the weights in the weighted sum. We evaluate the method across several experiments, including the Duffing oscillator and the Kuramoto-Sivashinsky equation, showcasing the method's different strengths.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 10","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149179623","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

Explaining the Fibonacci order in the period-doubling cascade to chaos. 解释周期加倍级联到混沌中的斐波那契数列。

IF 3.3 2区数学

Chaos Pub Date : 2026-10-01 DOI: 10.1063/5.0353533

Aarsh Chotalia, P Parmananda

引用次数: 0

Erratum: "Frequency-dependent response in cortical network with periodic electrical stimulation" [Chaos 30, 073130 (2020)]. 勘误：“周期性电刺激下皮层网络的频率依赖性响应”[混沌30,073130(2020)]。

IF 3.3 2区数学

Chaos Pub Date : 2026-10-01 DOI: 10.1063/5.0360826

Jixuan Wang, Bin Deng, Tianshi Gao, Jiang Wang, Guosheng Yi, Ruofan Wang

引用次数: 0

Data-driven reduced modeling of delayed dynamical systems via spectral submanifolds.

IF 3.3 2区数学

Chaos Pub Date : 2026-10-01 DOI: 10.1063/5.0344712

Giacomo Abbasciano, Gergely Buza, George Haller

引用次数: 0

Revisiting the dynamical properties of Pedlosky's two-layer model for finite amplitude baroclinic waves. 再论有限振幅斜压波的Pedlosky双层模型的动力学性质。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0339310

Nicolas De Ro, Jonathan Demaeyer, Stéphane Vannitsem

{"title":"Revisiting the dynamical properties of Pedlosky's two-layer model for finite amplitude baroclinic waves.","authors":"Nicolas De Ro, Jonathan Demaeyer, Stéphane Vannitsem","doi":"10.1063/5.0339310","DOIUrl":"https://doi.org/10.1063/5.0339310","url":null,"abstract":"Baroclinic instability is a fundamental mechanism driving atmospheric dynamics. In this work, we revisit Pedlosky's two-layer model for finite amplitude baroclinic waves-a seminal framework for studying the unstable growth of finite perturbations-leveraging modern nonlinear techniques and computational resources. We show that the geophysical state of the baroclinic wave exhibits a rich diversity of dynamical regimes governed by the level of dissipation induced by Ekman boundary layers. In the inviscid limit, we demonstrate that the model is integrable. Upon increasing dissipation, the system undergoes a complex sequence of bifurcations. On the one hand, deterministic chaos, identified by means of the Lyapunov exponents, provides a genuine mechanism for destabilization of the wave. On the other hand, in regimes where the wave equilibrates, dependence on the initial condition is crucial, eventually leading to the coexistence of multiple attractors. We study the governing equations of the model and their truncation to a finite-dimensional system of ordinary differential equations, together with the minimal low-order truncated system, which is structurally equivalent to the Lorenz model. Its bifurcation diagram elucidates the transition of the wave amplitude from stable equilibration to periodic oscillations-terminating in homoclinic orbits-and, ultimately, deterministic chaos through a period-doubling route. We finally comment on the robustness of these features for higher-dimensional models.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148967001","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

Discriminating disorders and their complexity. 鉴别障碍及其复杂性。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0341362

Jean Sire Armand Eyebe Fouda, Norbert Marwan, Jürgen Kurths, Wolfram Koepf

{"title":"Discriminating disorders and their complexity.","authors":"Jean Sire Armand Eyebe Fouda, Norbert Marwan, Jürgen Kurths, Wolfram Koepf","doi":"10.1063/5.0341362","DOIUrl":"https://doi.org/10.1063/5.0341362","url":null,"abstract":"Knowledge of the dynamics nature is essential for efficient system modeling, whereas the assessment of its complexity is useful for quantifying predictability. Depending on the nature of the information source, complexity can be ordered or disordered, although most existing methods do not specify this nature. In this paper, we present a novel determinism index as an efficient measure to determine the nature of data through the complexity of the ordinal pattern slope sum (sCOPSS). Combining the above index with the sCOPSS yields a comprehensive tool for estimating the complexity and disorder of short observations. Our results provide a negative complexity for deterministic data and a positive complexity for stochastic data and mixtures of stochastic and deterministic data, thus allowing identification among them. Mixing chaotic and stochastic data reveals a resonance phenomenon in sCOPSS that allows further reduction of the requirement for data length and improves the separability of the method. Applications to real-world data are given for the identification of audio signals and the classification of electrocardiogram beats. The results obtained confirm the effectiveness of the signed complexity for discriminating disorders and their complexity from short time series, thus separating sources in mixed data.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149073693","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

Semi-analytical switching-time control in a memristive FitzHugh-Nagumo circuit via an AD-IC PID architecture operated in the proportional limit. 基于AD-IC PID结构的忆阻式FitzHugh-Nagumo电路的半解析开关时间控制。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0352758

Yiğit Aydoğan, Elham Minayi

{"title":"Semi-analytical switching-time control in a memristive FitzHugh-Nagumo circuit via an AD-IC PID architecture operated in the proportional limit.","authors":"Yiğit Aydoğan, Elham Minayi","doi":"10.1063/5.0352758","DOIUrl":"https://doi.org/10.1063/5.0352758","url":null,"abstract":"The bang-bang adaptive law of a periodically forced memristive FitzHugh-Nagumo (FHN) circuit is replaced with a continuous energy-feedback controller formulated in a hardware-realizable form using the Add-Differentiate integrated circuit (AD-IC) proportional-integral-derivative architecture. The architecture is operated in the proportional limit (Ti = 109 and Td = 0), so the switching dynamics are governed by the proportional gain Kp while retaining a mapping to the AD-IC resistor ratio. Promoting the diversion-branch conductance parameter λ5 from a fixed scalar to a dynamical state driven by the controller output yields a six-dimensional closed-loop system. In the quasi-static limit, where λ5 evolves slowly relative to the FHN oscillation period, the time to drive the circuit from its high-energy firing mode to the quiescent low-energy state satisfies the semi-analytical relation τswitch=I(H∗)/Kp, where H∗ is the target energy and I(H∗) is an energy-landscape path integral evaluated numerically from quasi-static steady-state measurements. For a selected target, the inverse dependence on Kp = R1/R2 gives a closed-form gain-scaling rule that separates component selection from the application energy target. A feasibility boundary Hmax∗≈1.87 emerges from the minimum of the energy landscape along the approach path to the fold bifurcation; a two-branch bifurcation diagram confirms the wide bistable region in which both the firing mode and the quiescent mode coexist as stable attractors. Validation against 15 Runge-Kutta simulations across a two-dimensional (Kp,H∗) design space gives a mean absolute error of 14.7%, with systematic overestimation attributed to forcing-induced advance of the transition relative to the quasi-static fold point at larger gains.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149015832","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

Evolutionary games on higher-order networks. 高阶网络上的进化博弈。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0348359

Zihao Zhou, Haosen Wang, Jun Tang

{"title":"Evolutionary games on higher-order networks.","authors":"Zihao Zhou, Haosen Wang, Jun Tang","doi":"10.1063/5.0348359","DOIUrl":"https://doi.org/10.1063/5.0348359","url":null,"abstract":"Traditional evolutionary game theory often represents population structure with dyadic networks, although many applications require payoffs defined over groups. Hypergraphs and simplicial complexes retain group membership explicitly, but their effects must be distinguished from nonlinearities already present in multiplayer payoff functions. This structured scoping review separates these two sources of variation. A multiplayer nonlinear-payoff effect arises from thresholds, synergy, saturation, or heterogeneous group benefits on a fixed interaction structure. Such effects can occur in well-mixed or spatial groups without higher-order topology. A higher-order topological effect arises from explicit group membership, hyperedge overlap, inter-order organization, or simplicial closure. Its assessment requires the payoff, update rule, group-size distribution, and selection regime to be fixed or closely matched. A documented search through July 30, 2026 identified 85 core works: 80 primary studies and 5 conceptual or review articles. Across this evidence, nonlinear payoffs generate frequency dependence, internal equilibria, invasion thresholds, and, in some models, multistability. Higher-order topology instead changes group sharing, spillover between groups, and the routes to invasion or fixation. Discontinuous transitions and hysteresis are model outcomes whose origins depend on the complete payoff, topology, update, and feedback specification. Related graph-based research on fairness, trust, AI safety races, open-data stewardship, and cheap talk defines a broader agenda. Social welfare must also be evaluated separately from cooperation frequency. Direct empirical tests and factorial comparisons with matched baselines remain limited.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148873197","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

Chaos最新文献