IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0336997

Armand Sylvin Etémé, Alain Mvogo, Saralees Nadarajah, Henri Paul Ekobena Fouda, Timoléon Crépin Kofané, Conrad Bertrand Tabi

{"title":"Chimera states, synchronization, and energy consumption in a chaotic electrically coupled Hindmarsh-Rose neural network under multiple memory effects.","authors":"Armand Sylvin Etémé, Alain Mvogo, Saralees Nadarajah, Henri Paul Ekobena Fouda, Timoléon Crépin Kofané, Conrad Bertrand Tabi","doi":"10.1063/5.0336997","DOIUrl":"https://doi.org/10.1063/5.0336997","url":null,"abstract":"We investigate memory-induced collective dynamics in a ring of electrically coupled Hindmarsh-Rose neurons operating in a chaotic bursting regime. The effects of long-range interactions, diffusion delay, reaction delay, and electromagnetic induction on spatiotemporal organization and Hamiltonian energy density are systematically analyzed. The dynamics is quantified using five complementary statistical indicators: the synchronization factor, the strength of incoherence, the discontinuity measure, the skewness measure, and the time-averaged Hamiltonian energy density. Depending on the memory parameters, the network exhibits asynchronous, chimera, multichimera, and synchronized states. We show that long-range interactions increase the Hamiltonian energy density and enhance the level of collective activity, although they predominantly generate asynchronous states when acting alone. Diffusion delay generates a rich variety of collective states, ranging from asynchronous and chimera patterns to complete synchronization depending on the interaction range, while reaction delay predominantly supports asynchronous, chimera, and multichimera dynamics. In contrast, electromagnetic induction promotes global synchronization from a critical memristive coupling threshold. Furthermore, the Hamiltonian energy density increases monotonically with the interaction range, reaction delay, and memristive feedback strength, whereas it exhibits a non-monotonic dependence on diffusion delay. These findings demonstrate that multiple memory mechanisms interact synergistically and competitively to shape neuronal coordination, energy localization, and pattern formation, providing new insights into the design of robust neuromorphic systems and brain-inspired algorithms.","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":"148873162","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

Spiking neural networks based on a discrete second-order memristive synapse: Modeling, dynamics, and applications. 基于离散二阶记忆突触的脉冲神经网络：建模、动态和应用。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0343851

Tao Zhou, Xue Zhao, Minglin Ma

{"title":"Spiking neural networks based on a discrete second-order memristive synapse: Modeling, dynamics, and applications.","authors":"Tao Zhou, Xue Zhao, Minglin Ma","doi":"10.1063/5.0343851","DOIUrl":"https://doi.org/10.1063/5.0343851","url":null,"abstract":"Discrete-time spiking neural networks provide an important framework for modeling discrete memristive synapses and for investigating their spike transmission and network dynamical behaviors. However, existing studies mostly focus on single-state discrete memristive synapses, and systematic research on second-order discrete memristive synapses in discrete-time spiking neural networks is still relatively scarce. Based on this, this paper constructs a second-order discrete memristive synapse model regulated by two internal-state variables in a coordinated manner. First, the basic dynamic characteristics of the proposed synapse model are analyzed, and its state evolution features and numerical stability performance under random spike input conditions are investigated. Subsequently, the model is embedded into a typical discrete neuron model for unified verification, and the results show that it can achieve stable pulse transmission. Furthermore, the influence of memristive synapse parameters and coupling strength on synchronization behavior is examined at the network level. The results indicate that the system can evolve from incomplete synchronization to high synchronization and exhibit chimera-like states in a ring-coupled network. Additionally, this paper conducts pulse coding, limited pattern discrimination, and spike-timing-dependent plasticity analysis based on the proposed synapse model. The results show that the model can maintain a certain information representation and pattern-discrimination ability under noise interference, providing a feasible solution for the stable modeling of memristive synapses and their information-processing applications in discrete spiking neural networks.","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":"148879236","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

Broad onset of chaos with toroidal dynamics in finite-size random neural networks. 有限大小随机神经网络中具有环面动力学的广义混沌。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0341330

Hiromichi Suetani

引用次数: 0

Emergence of statistical financial factors by a diffusion process. 由扩散过程产生的统计金融因素。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0338836

Jose Negrete, Jaime J Ramos

{"title":"Emergence of statistical financial factors by a diffusion process.","authors":"Jose Negrete, Jaime J Ramos","doi":"10.1063/5.0338836","DOIUrl":"https://doi.org/10.1063/5.0338836","url":null,"abstract":"Factor models provide a representation of the joint behavior of large cross sections of financial assets through a reduced set of underlying drivers. In this work, we propose a network-based dynamical framework in which statistical factors emerge endogenously from interactions among assets, rather than being imposed exogenously or extracted purely statistically. We model asset returns as a system of coupled nonlinear maps influenced by a network of interactions encoded in a coupling matrix. This matrix is constructed via an orthogonal transformation of a Laplacian operator with prescribed nullity, allowing us to control the system's effective dimensionality. Under appropriate coupling conditions, the dynamics reduce from a high-dimensional phase space to a lower-dimensional invariant manifold, where synchronization modes of co-movement arise. We show that the number of emergent statistical factors is directly related to the nullity of the coupling matrix, consistent with a stability analysis performed here. Simulations demonstrate that the model reproduces key stylized features of financial returns while generating factors with balanced loadings across assets. Finally, we show that this model reproduces features that are observed in an empirical portfolio. These findings suggest that statistical factors can be interpreted as emergent synchronization modes of an interacting nonlinear system, providing a complementary perspective to the existing economic and statistical factor 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":"148879268","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

Arnold tongues and stochastic masking in an autonomously embedded ENSO recharge oscillator. 自主嵌入ENSO充电振荡器中的Arnold舌和随机掩蔽。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0350115

Lenka Přibylová, Eva Kopřivová

{"title":"Arnold tongues and stochastic masking in an autonomously embedded ENSO recharge oscillator.","authors":"Lenka Přibylová, Eva Kopřivová","doi":"10.1063/5.0350115","DOIUrl":"https://doi.org/10.1063/5.0350115","url":null,"abstract":"The El Niño-Southern Oscillation (ENSO) displays a characteristic combination of seasonal phase locking, interannual variability and irregular event-to-event changes in amplitude and return time. We study these features in a seasonally forced nonlinear recharge oscillator from the viewpoint of bifurcation theory of periodic orbits. The explicitly time-periodic growth-rate modulation is transformed into an autonomous system by embedding the annual forcing into a supercritical Hopf oscillator. This formulation makes the model directly accessible to numerical continuation and Floquet analysis. We show that the annual cycle creates a resonance skeleton organized by Neimark-Sacker bifurcations, resonance points that are branch points of limit cycles and limit-point-of-cycle boundaries of Arnold tongues. The linear recharge-discharge frequency controls the location of the 1:n resonance roots, while the forcing amplitude determines the width and robustness of the corresponding tongues. Locked solutions appear as closed periodic orbits on the torus, whereas parameter values outside the Arnold tongues produce quasiperiodic motion. Slow drift of the recharge-discharge frequency causes transient capture into and escape from distinct 1:n regimes, and state-dependent stochastic forcing masks the deterministic periodic backbone by perturbing trajectories away from locked cycles. The resulting framework interprets irregular ENSO-like variability not as the absence of structure, but as a noise-perturbed system moving through a structured resonance landscape. A comparison with the Relative Oceanic Niño Index is used as an illustrative observational signature of transient phase locking rather than as a statistical attribution claim.","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":"148944391","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

Subject-specific data-driven parameterization of preclinical 3D MRI-based heart models using an efficient algorithm to predict infarct-related tachycardia. 使用有效算法预测梗死相关心动过速的临床前3D mri心脏模型的受试者特定数据驱动参数化。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0336480

Jairo Rodríguez Padilla, Nicolas Cedilnik, Buntheng Ly, Graham A Wright, Mihaela Pop, Maxime Sermesant

{"title":"Subject-specific data-driven parameterization of preclinical 3D MRI-based heart models using an efficient algorithm to predict infarct-related tachycardia.","authors":"Jairo Rodríguez Padilla, Nicolas Cedilnik, Buntheng Ly, Graham A Wright, Mihaela Pop, Maxime Sermesant","doi":"10.1063/5.0336480","DOIUrl":"10.1063/5.0336480","url":null,"abstract":"The computational efficiency of contemporary multi-scale digital twins used to investigate cardiac arrhythmia is often hindered by the equation system complexity, while the accuracy of predictions depends on the calibration of model parameters and their intricate non-linear relation. Here we employed a robust pipeline for fast simulations of scar-related ventricular tachycardia (VT) inducibility using an efficient Lattice-Boltzmann Method with GPU-based accelerated code. We tested the pipeline on 3D digital twins built from MR images acquired in n = 8 swine with chronic infarction, by performing a subject-specific personalization of each model per tissue type (i.e., scar, border zone, and healthy) and tuning the key parameters (e.g., action potential duration, excitability, and wave speed) from recorded endocardial bipolar voltage maps and intracardiac electrograms. We first validated the VT simulation outcome by precisely replicating the stimulation protocol and pacing site used in the animal studies. Our results demonstrated very good agreement between the experiment and simulated VT outcome for personalized model parameters using subject-specific values, compared to a poor outcome when parameters were tuned from average values from all cases. Second, we performed a comprehensive in silico study where the stimulation was delivered from 10 000 virtual endocardial locations and found a strong dependence of VT (non)/-inducibility per case on the stimulation site. Simulating 10 s of sustained VT induced on a 3D model comprising 1.2 million cubic voxels (0.7 mm edge size) took 30 min on a laptop using GPU, underlying the computational tractability of our pipeline and its potential clinical translation to predict infarct-related VT risk.","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":"148879336","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

Spectral stability correspondence between networks and continuous media: Theory and applications to population dynamics. 网络和连续介质之间的光谱稳定性对应关系：种群动态的理论和应用。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0349270

Idan Sorin, Alexander Nepomnyashchy

{"title":"Spectral stability correspondence between networks and continuous media: Theory and applications to population dynamics.","authors":"Idan Sorin, Alexander Nepomnyashchy","doi":"10.1063/5.0349270","DOIUrl":"https://doi.org/10.1063/5.0349270","url":null,"abstract":"We investigate the stability of synchronized oscillations in coupled nonlinear systems by establishing a spectral correspondence between continuous linear shift-invariant (LSI) media and discrete networks. In this framework, Fourier modes of a continuous spatial operator and eigenmodes of a network coupling matrix are treated as spectral parameters of the same master stability function. This correspondence allows finite-wavenumber instabilities of continuous media to be translated into predictable instability windows in the network coupling space. Applying the framework to zero-row-sum Metzler coupling matrices and using a competitive Lotka-Volterra model as a paradigm, we show that synchronization may exhibit reentrant behavior: it is stable for weak coupling, lost within intermediate coupling intervals, and restored at stronger coupling. The framework also reveals a distinction between undirected and directed networks. For undirected networks, the relevant spectra are real and the resulting instability mechanism is analogous to that of standard reaction-diffusion systems with real wavenumbers. Directed networks, however, can possess complex spectra. We show that such complex spectral modes can induce quasiperiodic bifurcations of the synchronized state, leading to dynamical regimes that are inaccessible to standard real-wavenumber reflection-invariant reaction-diffusion 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":"148891132","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

Structure-aware learning of Poincaré return dynamics via symbolic decomposition. 基于符号分解的poincarcars返回动态的结构感知学习。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0347566

Mengzhao Jin, Jana Rodriguez Hertz, Hong-Kun Zhang

{"title":"Structure-aware learning of Poincaré return dynamics via symbolic decomposition.","authors":"Mengzhao Jin, Jana Rodriguez Hertz, Hong-Kun Zhang","doi":"10.1063/5.0347566","DOIUrl":"https://doi.org/10.1063/5.0347566","url":null,"abstract":"We develop a data-driven framework for approximating the first same-direction return time and the associated Poincaré map of chaotic flows. Learning these quantities is challenging because the return-time field may exhibit sharp localized variations, and nearby initial conditions may undergo qualitatively different pre-return excursions. We introduce a symbolic residual-learning strategy based on finite itineraries of transverse section crossings. A global neural network captures the dominant trend, and a classifier routes class-dependent residual corrections through soft or hard rules. Reflection symmetry is incorporated using a symmetry-aware input representation and symmetry-reduced symbolic classes, while the predicted return time is supplied as an auxiliary feature to the Poincaré-map model. Experiments on the Lorenz and Shimizu-Morioka systems show that the global configuration using a logarithmic return-time target and a symmetry-aware input representation improves accuracy, while symbolic residual correction further reduces errors, especially in high-gradient regions. The return-time input also provides useful information for learning the Poincaré map, although the resulting gains are system dependent. The results reveal a qualitative correspondence between prominent return-time gradients and finite symbolic-class boundaries, supporting symbolic decomposition as a structured approach to learning chaotic return dynamics.","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":"148905157","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

Simplicial SEIQS epidemic dynamics: Bistability and backward bifurcation under a mean-field approximation. 简单SEIQS流行动力学：平均场近似下的双稳定性和后向分岔。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0346196

Bei Sun, Chi K Tse

{"title":"Simplicial SEIQS epidemic dynamics: Bistability and backward bifurcation under a mean-field approximation.","authors":"Bei Sun, Chi K Tse","doi":"10.1063/5.0346196","DOIUrl":"https://doi.org/10.1063/5.0346196","url":null,"abstract":"We investigate the impact of higher-order, or simplicial, interactions on the mean-field dynamics of a susceptible-exposed-infectious-quarantined-susceptible epidemic model on networks, under a degree-homogeneous mean-field approximation. For the corresponding mean-field system, we derive explicit conditions for the existence and local asymptotic stability of disease-free and endemic equilibria, and obtain closed-form expressions for the critical parameters β0, βc, and vc that govern the onset of subthreshold bistability. The analysis shows that the simplicial transmission coefficient does not alter the linear epidemic threshold, but it can create a bistable regime below βc in which the disease-free equilibrium coexists with two endemic equilibria. We then perform a numerical bifurcation and basin analysis combining equilibrium branches, phase diagrams, time-domain simulations, and basin-of-attraction plots. These results reveal how higher-order interactions enlarge the endemic equilibrium and induce a nontrivial separatrix between extinction and persistence. Finally, a Routh-Hurwitz analysis excludes a Hopf bifurcation of the larger endemic equilibrium under the baseline parameters, while numerical scans over wider parameter ranges provide additional support for the absence of Hopf instability in the tested regimes. The findings suggest that simplicial interactions enrich epidemic dynamics primarily through multistability and basin geometry rather than sustained oscillations, although oscillatory behavior in substantially different regimes remains possible.","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":"148905154","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

On the steady and breathing propagation of 2D flame-balls. 二维火球的稳定呼吸传播。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0340083

Jorge Yanez, Mike Kuznetsov

引用次数: 0

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