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Regular and Chaotic Dynamics最新文献

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Quasi-Periodic Parametric Perturbations of Two-Dimensional Hamiltonian Systems with Nonmonotonic Rotation 具有非单调旋转的二维哈密顿系统的准周期参数扰动
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010052
Kirill E. Morozov, Albert D. Morozov
{"title":"Quasi-Periodic Parametric Perturbations of Two-Dimensional Hamiltonian Systems with Nonmonotonic Rotation","authors":"Kirill E. Morozov,&nbsp;Albert D. Morozov","doi":"10.1134/S1560354724010052","DOIUrl":"10.1134/S1560354724010052","url":null,"abstract":"<div><p>We study nonconservative quasi-periodic (with <span>(m)</span> frequencies) perturbations of two-dimensional Hamiltonian systems with nonmonotonic rotation. It is assumed that the perturbation contains the so-called <i>parametric</i> terms. The behavior of solutions in the vicinity of degenerate resonances is described. Conditions for the existence of resonance <span>((m+1))</span>-dimensional invariant tori for which there are no generating ones in the unperturbed system are found. The class of perturbations for which such tori can exist is indicated. The results are applied to the asymmetric Duffing equation under a parametric quasi-periodic perturbation.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"65 - 77"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Universal Transient Dynamics in Oscillatory Network Models of Epileptic Seizures 癫痫发作振荡网络模型中的通用瞬态动力学
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S156035472401012X
Anton A. Kapustnikov, Marina V. Sysoeva, Ilya V. Sysoev
{"title":"Universal Transient Dynamics in Oscillatory Network Models of Epileptic Seizures","authors":"Anton A. Kapustnikov,&nbsp;Marina V. Sysoeva,&nbsp;Ilya V. Sysoev","doi":"10.1134/S156035472401012X","DOIUrl":"10.1134/S156035472401012X","url":null,"abstract":"<div><p>Discharges of different epilepsies are characterized by different signal shape and duration.\u0000The authors adhere to the hypothesis that spike-wave discharges are long transient processes rather than attractors. This helps to explain some experimentally observed properties of discharges, including the\u0000absence of a special termination mechanism and quasi-regularity.\u0000Analytical approaches mostly cannot be applied to studying transient dynamics in large networks. Therefore, to test the observed phenomena for universality one has to show that the same results can be achieved using different model types for nodes and different connectivity terms. Here, we study a class of simple network\u0000models of a thalamocortical system and show that for the same connectivity matrices long, but finite in time quasi-regular processes mimicking epileptic spike-wave discharges can be found using nodes described by three neuron models: FitzHugh – Nagumo, Morris – Lecar and Hodgkin – Huxley. This result\u0000takes place both for linear and nonlinear sigmoid coupling.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"190 - 204"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Classification of Axiom A Diffeomorphisms with Orientable Codimension One Expanding Attractors and Contracting Repellers 具有可定向一维扩展吸引子和收缩排斥子的公理 A 衍变的分类
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S156035472401009X
Vyacheslav Z. Grines, Vladislav S. Medvedev, Evgeny V. Zhuzhoma
{"title":"Classification of Axiom A Diffeomorphisms with Orientable Codimension One Expanding Attractors and Contracting Repellers","authors":"Vyacheslav Z. Grines,&nbsp;Vladislav S. Medvedev,&nbsp;Evgeny V. Zhuzhoma","doi":"10.1134/S156035472401009X","DOIUrl":"10.1134/S156035472401009X","url":null,"abstract":"<div><p>Let <span>(mathbb{G}_{k}^{cod1}(M^{n}))</span>, <span>(kgeqslant 1)</span>, be the set of axiom A diffeomorphisms such that\u0000the nonwandering set of any <span>(finmathbb{G}_{k}^{cod1}(M^{n}))</span> consists of <span>(k)</span> orientable connected codimension one expanding attractors and contracting repellers where <span>(M^{n})</span> is a closed orientable <span>(n)</span>-manifold, <span>(ngeqslant 3)</span>. We classify the diffeomorphisms from <span>(mathbb{G}_{k}^{cod1}(M^{n}))</span> up to the global conjugacy on nonwandering sets. In addition, we show that any <span>(finmathbb{G}_{k}^{cod1}(M^{n}))</span> is <span>(Omega)</span>-stable and is not structurally stable. One describes the topological structure of a supporting manifold <span>(M^{n})</span>.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"143 - 155"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Sensitivity and Chaoticity of Some Classes of Semigroup Actions 几类半群作用的敏感性和混沌性
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010118
Nina I. Zhukova
{"title":"Sensitivity and Chaoticity of Some Classes of Semigroup Actions","authors":"Nina I. Zhukova","doi":"10.1134/S1560354724010118","DOIUrl":"10.1134/S1560354724010118","url":null,"abstract":"<div><p>The focus of the work is the investigation of chaos and closely related dynamic properties of continuous actions of almost open\u0000semigroups and <span>(C)</span>-semigroups. The class of dynamical systems <span>((S,X))</span> defined by such semigroups <span>(S)</span> is denoted by <span>(mathfrak{A})</span>.\u0000These semigroups contain, in particular, cascades, semiflows and groups of homeomorphisms. We extend the Devaney definition of chaos to general dynamical systems. For <span>((S,X)inmathfrak{A})</span> on locally compact metric spaces <span>(X)</span> with a countable base we\u0000prove that topological transitivity and density of the set formed by points having closed orbits imply the sensitivity to initial conditions. We assume neither the compactness of metric space nor the compactness of the above-mentioned closed orbits.\u0000In the case when the set of points having compact orbits is dense, our proof proceeds without the assumption of local compactness of the phase space <span>(X)</span>. This statement generalizes the well-known result of J. Banks et al. on Devaney’s definition\u0000of chaos for cascades.The interrelation of sensitivity, transitivity and the property of minimal sets of semigroups is investigated. Various examples are given.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"174 - 189"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Slow-Fast Systems with an Equilibrium Near the Folded Slow Manifold 在折叠慢速歧面附近达到平衡的慢-快系统
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-12-19 DOI: 10.1134/S156035472354002X
Natalia G. Gelfreikh, Alexey V. Ivanov
{"title":"Slow-Fast Systems with an Equilibrium Near the Folded Slow Manifold","authors":"Natalia G. Gelfreikh,&nbsp;Alexey V. Ivanov","doi":"10.1134/S156035472354002X","DOIUrl":"10.1134/S156035472354002X","url":null,"abstract":"<div><p>We study a slow-fast system with two slow and one fast variables.\u0000We assume that the slow manifold of the system possesses a fold and there is an equilibrium of the system in a small neighborhood of the fold. We derive a normal form for the system\u0000in a neighborhood of the pair “equilibrium-fold”\u0000and study the dynamics of the normal form. In particular, as the ratio of two time scales tends to zero we obtain an asymptotic formula for the Poincaré map\u0000and calculate the parameter values for the first period-doubling bifurcation. The theory is applied to a generalization of the FitzHugh – Nagumo system.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 2","pages":"376 - 403"},"PeriodicalIF":0.8,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138743675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Hyperbolic Attractors Which are Anosov Tori 属于阿诺索夫环的双曲吸引子
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-12-19 DOI: 10.1134/S1560354723540018
Marina K. Barinova, Vyacheslav Z. Grines, Olga V. Pochinka, Evgeny V. Zhuzhoma
{"title":"Hyperbolic Attractors Which are Anosov Tori","authors":"Marina K. Barinova,&nbsp;Vyacheslav Z. Grines,&nbsp;Olga V. Pochinka,&nbsp;Evgeny V. Zhuzhoma","doi":"10.1134/S1560354723540018","DOIUrl":"10.1134/S1560354723540018","url":null,"abstract":"<div><p>We consider a topologically mixing hyperbolic attractor <span>(Lambdasubset M^{n})</span> for a diffeomorphism <span>(f:M^{n}to M^{n})</span> of a compact orientable <span>(n)</span>-manifold <span>(M^{n})</span>, <span>(n&gt;3)</span>. Such an attractor <span>(Lambda)</span> is called an Anosov torus provided the restriction <span>(f|_{Lambda})</span> is conjugate to Anosov algebraic automorphism of <span>(k)</span>-dimensional torus <span>(mathbb{T}^{k})</span>.\u0000We prove that <span>(Lambda)</span> is an Anosov torus for two cases:\u00001) <span>(dim{Lambda}=n-1)</span>, <span>(dim{W^{u}_{x}}=1)</span>, <span>(xinLambda)</span>;\u00002) <span>(dimLambda=k,dim W^{u}_{x}=k-1,xinLambda)</span>, and <span>(Lambda)</span> belongs to an <span>(f)</span>-invariant closed <span>(k)</span>-manifold, <span>(2leqslant kleqslant n)</span>, topologically embedded in <span>(M^{n})</span>.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 2","pages":"369 - 375"},"PeriodicalIF":0.8,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138743744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 and Hyperchaos in Two Coupled Identical Hindmarsh – Rose Systems 两个完全相同的辛德马什-罗斯耦合系统中的混沌与超混沌
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-12-19 DOI: 10.1134/S1560354723540031
Nataliya V. Stankevich, Andrey A. Bobrovskii, Natalya A. Shchegoleva
{"title":"Chaos and Hyperchaos in Two Coupled Identical Hindmarsh – Rose Systems","authors":"Nataliya V. Stankevich,&nbsp;Andrey A. Bobrovskii,&nbsp;Natalya A. Shchegoleva","doi":"10.1134/S1560354723540031","DOIUrl":"10.1134/S1560354723540031","url":null,"abstract":"<div><p>The dynamics of two coupled neuron models, the Hindmarsh – Rose systems, are studied. Their\u0000interaction is simulated via a chemical coupling that is implemented with a sigmoid function.\u0000It is shown that the model may exhibit complex behavior: quasi-periodic, chaotic and\u0000hyperchaotic oscillations. A phenomenological scenario for the formation of hyperchaos\u0000associated with the appearance of a discrete Shilnikov attractor is described. It is shown\u0000that the formation of these attractors leads to the appearance of in-phase bursting\u0000oscillations.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"120 - 133"},"PeriodicalIF":0.8,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138745924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Non-Quasi-Periodic Normal Form Theory 非准周期正态理论
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-12-07 DOI: 10.1134/S1560354723060035
Gabriella Pinzari
{"title":"Non-Quasi-Periodic Normal Form Theory","authors":"Gabriella Pinzari","doi":"10.1134/S1560354723060035","DOIUrl":"10.1134/S1560354723060035","url":null,"abstract":"<div><p>We review a recent application of the ideas of normal form theory to systems (Hamiltonian ones or general ODEs) where the perturbing term is not periodic in one coordinate variable. The main difference\u0000from the standard case consists in the non-uniqueness of the normal form and the total absence of the small\u0000divisors problem. The exposition is quite general, so as to allow extensions to the case\u0000of more non-periodic coordinates, and more functional settings. Here, for simplicity,\u0000we work in the real-analytic class.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 6","pages":"841 - 864"},"PeriodicalIF":0.8,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138555304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Unifying the Hyperbolic and Spherical (2)-Body Problem with Biquaternions 用双四元数统一双曲和球面 $$2$ 天体问题
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-12-07 DOI: 10.1134/S1560354723060011
Philip Arathoon
{"title":"Unifying the Hyperbolic and Spherical (2)-Body Problem with Biquaternions","authors":"Philip Arathoon","doi":"10.1134/S1560354723060011","DOIUrl":"10.1134/S1560354723060011","url":null,"abstract":"<div><p>The <span>(2)</span>-body problem on the sphere and hyperbolic space are both real forms of holomorphic Hamiltonian systems defined on the complex sphere. This admits a natural description in terms of biquaternions and allows us to address questions concerning the hyperbolic system by complexifying it and treating it as the complexification of a spherical system. In this way, results for the <span>(2)</span>-body problem on the sphere are readily translated to the hyperbolic case. For instance, we implement this idea to completely classify the relative equilibria for the <span>(2)</span>-body problem on hyperbolic 3-space and discuss their stability for a strictly attractive potential.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 6","pages":"822 - 834"},"PeriodicalIF":0.8,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138555416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Method of Introduction of Local Variables in a Neighborhood of Periodic Solution of a Hamiltonian System with Two Degrees of Freedom 论在具有两个自由度的哈密尔顿系统的周期解邻域中引入局部变量的方法
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-12-07 DOI: 10.1134/S1560354723060059
Boris S. Bardin
{"title":"On the Method of Introduction of Local Variables in a Neighborhood of Periodic Solution of a Hamiltonian System with Two Degrees of Freedom","authors":"Boris S. Bardin","doi":"10.1134/S1560354723060059","DOIUrl":"10.1134/S1560354723060059","url":null,"abstract":"<div><p>A general method is presented for constructing a nonlinear canonical transformation, which makes it possible to introduce local variables in a neighborhood of periodic motions of an autonomous Hamiltonian system with two degrees of freedom. This method can be used for investigating the behavior of the Hamiltonian system in\u0000the vicinity of its periodic trajectories. In particular, it can be applied to solve the problem of orbital stability of periodic motions.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 6","pages":"878 - 887"},"PeriodicalIF":0.8,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138563720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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