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Regular and Chaotic Dynamics最新文献

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Synchronization and Chaos in Adaptive Kuramoto Networks with Higher-Order Interactions: A Review 具有高阶相互作用的自适应Kuramoto网络的同步与混沌研究综述
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-02-18 DOI: 10.1134/S1560354725010046
Anastasiia A. Emelianova, Vladimir I. Nekorkin
{"title":"Synchronization and Chaos in Adaptive Kuramoto Networks with Higher-Order Interactions: A Review","authors":"Anastasiia A. Emelianova,&nbsp;Vladimir I. Nekorkin","doi":"10.1134/S1560354725010046","DOIUrl":"10.1134/S1560354725010046","url":null,"abstract":"<div><p>This paper provides an overview of the results obtained from the study of adaptive dynamical networks of Kuramoto oscillators with higher-order interactions. The main focus is on results in the field of synchronization and collective chaotic dynamics. Identifying the dynamical mechanisms underlying the synchronization of oscillator ensembles with higher-order interactions may contribute to further advances in understanding the work of some complex systems such as the neural networks of the brain.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 1","pages":"57 - 75"},"PeriodicalIF":0.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145122057","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 Structure of Orbits from a Neighborhood of a Transversal Homoclinic Orbit to a Nonhyperbolic Fixed Point 横向同斜轨道邻域到非双曲不动点的轨道结构
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-02-18 DOI: 10.1134/S1560354725010022
Sergey V. Gonchenko, Ol’ga V. Gordeeva
{"title":"On the Structure of Orbits from a Neighborhood of a Transversal Homoclinic Orbit to a Nonhyperbolic Fixed Point","authors":"Sergey V. Gonchenko,&nbsp;Ol’ga V. Gordeeva","doi":"10.1134/S1560354725010022","DOIUrl":"10.1134/S1560354725010022","url":null,"abstract":"<div><p>We consider a one-parameter family <span>(f_{mu})</span> of multidimensional diffeomorphisms such that for <span>(mu=0)</span> the diffeomorphism <span>(f_{0})</span> has a transversal homoclinic orbit to a nonhyperbolic fixed point of arbitrary finite order <span>(ngeqslant 1)</span> of degeneracy, and for <span>(mu&gt;0)</span> the fixed point becomes a hyperbolic saddle. In the paper, we give a complete description of the structure of the set <span>(N_{mu})</span> of all orbits entirely lying in a sufficiently small fixed neighborhood of the homoclinic orbit. Moreover, we show that for <span>(mugeqslant 0)</span> the set <span>(N_{mu})</span> is hyperbolic (for <span>(mu=0)</span> it is nonuniformly hyperbolic) and the dynamical system <span>(f_{mu}bigl{|}_{N_{mu}})</span> (the restriction of <span>(f_{mu})</span> to <span>(N_{mu})</span>) is topologically conjugate to a certain nontrivial subsystem of the topological Bernoulli scheme of two symbols.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 1","pages":"9 - 25"},"PeriodicalIF":0.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145122058","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
Local and Nonlocal Cycles in a System with Delayed Feedback Having Compact Support 具有紧支持的时滞反馈系统中的局部环和非局部环
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-02-18 DOI: 10.1134/S1560354725010058
Alexandra A. Kashchenko, Sergey A. Kashchenko
{"title":"Local and Nonlocal Cycles in a System with Delayed Feedback Having Compact Support","authors":"Alexandra A. Kashchenko,&nbsp;Sergey A. Kashchenko","doi":"10.1134/S1560354725010058","DOIUrl":"10.1134/S1560354725010058","url":null,"abstract":"<div><p>The purpose of this work is to study small oscillations and oscillations with an asymptotically large amplitude in nonlinear systems of two equations with delay, regularly depending on a small parameter. We assume that the nonlinearity is compactly supported, i. e., its action is carried out only in a certain finite region of phase space.\u0000Local oscillations are studied by classical methods of bifurcation theory, and the study of nonlocal dynamics is based on a special large-parameter method, which makes it possible to reduce the original problem to the analysis of a specially constructed finite-dimensional mapping. In all cases, algorithms for constructing the asymptotic behavior of solutions are developed. In the case of local analysis, normal forms are constructed that determine the dynamics of the original system in a neighborhood of the zero equilibrium state, the asymptotic behavior of the periodic solution is constructed, and the question of its stability is answered. In studying nonlocal\u0000solutions, one-dimensional mappings are constructed that make it possible to determine\u0000the behavior of solutions with an asymptotically large amplitude. Conditions for the\u0000existence of a periodic solution are found and its stability is investigated.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 1","pages":"103 - 119"},"PeriodicalIF":0.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145122075","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
Dynamics of Slow-Fast Hamiltonian Systems: The Saddle–Focus Case 慢-快哈密顿系统动力学：鞍-焦点情况
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-12-27 DOI: 10.1134/S1560354724590039
Sergey V. Bolotin
{"title":"Dynamics of Slow-Fast Hamiltonian Systems: The Saddle–Focus Case","authors":"Sergey V. Bolotin","doi":"10.1134/S1560354724590039","DOIUrl":"10.1134/S1560354724590039","url":null,"abstract":"<div><p>We study the dynamics of a multidimensional slow-fast Hamiltonian system in a neighborhood\u0000of the slow manifold under the assumption that the frozen system has a hyperbolic equilibrium\u0000with complex simple leading eigenvalues\u0000and there exists a transverse homoclinic orbit.\u0000We obtain formulas for the corresponding Shilnikov separatrix map\u0000and prove the existence of trajectories in a neighborhood of the homoclinic set\u0000with a prescribed evolution of the slow variables.\u0000An application to the <span>(3)</span> body problem is given.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 1","pages":"76 - 92"},"PeriodicalIF":0.8,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145122441","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
Rolling of a Homogeneous Ball on a Moving Cylinder 在运动的圆筒上滚动均匀的球
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-12-27 DOI: 10.1134/S1560354724590027
Alexander A. Kilin, Elena N. Pivovarova, Tatiana B. Ivanova
{"title":"Rolling of a Homogeneous Ball on a Moving Cylinder","authors":"Alexander A. Kilin,&nbsp;Elena N. Pivovarova,&nbsp;Tatiana B. Ivanova","doi":"10.1134/S1560354724590027","DOIUrl":"10.1134/S1560354724590027","url":null,"abstract":"<div><p>This paper addresses the problem of a homogeneous ball rolling on the inner surface of a\u0000circular cylinder in a field of gravity parallel to its axis. It is assumed that the ball\u0000rolls without slipping on the surface of the cylinder, and that the cylinder executes\u0000plane-parallel motions in a circle perpendicular to its symmetry axis. The integrability of\u0000the problem by quadratures is proved. It is shown that in this problem the trajectories of\u0000the ball are quasi-periodic in the general case, and that an unbounded elevation of the ball\u0000is impossible. However, in contrast to a fixed (or rotating) cylinder, there exist resonances\u0000at which the ball moves on average downward with constant acceleration.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"628 - 638"},"PeriodicalIF":0.8,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145122456","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 Stability of Discrete (N+1) Vortices in a Two-Layer Rotating Fluid: The Cases (N=4,5,6) 两层旋转流体中离散(N+1)涡旋的稳定性 (N=4,5,6)
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-12-20 DOI: 10.1134/S1560354724580019
Leonid G. Kurakin, Irina V. Ostrovskaya, Mikhail A. Sokolovskiy
{"title":"On the Stability of Discrete (N+1) Vortices in a Two-Layer Rotating Fluid: The Cases (N=4,5,6)","authors":"Leonid G. Kurakin,&nbsp;Irina V. Ostrovskaya,&nbsp;Mikhail A. Sokolovskiy","doi":"10.1134/S1560354724580019","DOIUrl":"10.1134/S1560354724580019","url":null,"abstract":"<div><p>A two-layer quasigeostrophic model is considered in the <span>(f)</span>-plane approximation. The stability of a discrete axisymmetric vortex structure is analyzed for the case where the structure consists of a central vortex of arbitrary effective intensity <span>(Gamma)</span> and <span>(N)</span> (<span>(N=4,5)</span> and <span>(6)</span>) identical peripheral vortices. The identical vortices, each having a unit effective intensity, are uniformly distributed over a circle of radius <span>(R)</span> in the lower layer. The central vortex lies either in the same or in another layer. The problem has three parameters <span>((R,Gamma,alpha))</span>, where <span>(alpha)</span> is the difference between layer nondimensional thicknesses. The cases <span>(N=2,3)</span> were investigated by us earlier.</p><p>The theory of stability of steady-state motions of dynamical systems with a continuous symmetry group <span>(mathcal{G})</span> is applied. The two definitions of stability used in the study are Routh stability and <span>(mathcal{G})</span>-stability.\u0000The Routh stability is the stability of a one-parameter orbit of a steady-state rotation of a\u0000vortex structure, and the <span>(mathcal{G})</span>-stability is the stability of a three-parameter invariant set <span>(O_{mathcal{G}})</span>, formed by the orbits of a continuous family of steady-state rotations of a two-layer vortex structure.\u0000The problem of Routh stability is reduced to the problem of stability of a family of\u0000equilibria of a Hamiltonian system. The quadratic part of the Hamiltonian and the eigenvalues of the linearization matrix are studied analytically.</p><p>The results of theoretical analysis are sustained by numerical calculations of vortex trajectories.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 3","pages":"325 - 353"},"PeriodicalIF":0.8,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166838","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 Existence of Expanding Attractors with Different Dimensions 关于不同维数膨胀吸引子的存在性
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-12-20 DOI: 10.1134/S1560354724580020
Vladislav S. Medvedev, Evgeny V. Zhuzhoma
{"title":"On the Existence of Expanding Attractors with Different Dimensions","authors":"Vladislav S. Medvedev,&nbsp;Evgeny V. Zhuzhoma","doi":"10.1134/S1560354724580020","DOIUrl":"10.1134/S1560354724580020","url":null,"abstract":"<div><p>We prove that an <span>(n)</span>-sphere <span>(mathbb{S}^{n})</span>, <span>(ngeqslant 2)</span>, admits structurally stable diffeomorphisms <span>(mathbb{S}^{n}tomathbb{S}^{n})</span> with nonorientable expanding attractors of any topological dimension <span>(din{1,ldots,[frac{n}{2}]})</span> where <span>([x])</span> is the integer part of <span>(x)</span>. In addition, any <span>(n)</span>-sphere <span>(mathbb{S}^{n})</span>, <span>(ngeqslant 3)</span>, admits axiom A diffeomorphisms <span>(mathbb{S}^{n}tomathbb{S}^{n})</span> with orientable expanding attractors of any topological dimension <span>(din{1,ldots,[frac{n}{3}]})</span>. We prove that an <span>(n)</span>-torus <span>(mathbb{T}^{n})</span>, <span>(ngeqslant 2)</span>, admits structurally stable diffeomorphisms <span>(mathbb{T}^{n}tomathbb{T}^{n})</span> with orientable expanding attractors of any topological dimension <span>(din{1,ldots,n-1})</span>. We also prove that, given any closed <span>(n)</span>-manifold <span>(M^{n})</span>, <span>(ngeqslant 2)</span>, and any <span>(din{1,ldots,[frac{n}{2}]})</span>, there is an axiom A diffeomorphism <span>(f:M^{n}to M^{n})</span> with a <span>(d)</span>-dimensional nonorientable expanding attractor. Similar statements hold for axiom A flows.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 1","pages":"93 - 102"},"PeriodicalIF":0.8,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145122182","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 a Quadratic Poisson Algebra and Integrable Lotka – Volterra Systems with Solutions in Terms of Lambert’s (W) Function 二阶泊松代数和可积Lotka - Volterra系统的Lambert (W)函数解
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-12-20 DOI: 10.1134/S1560354724580032
Peter H. van der Kamp, David I. McLaren, G. R. W. Quispel
{"title":"On a Quadratic Poisson Algebra and Integrable Lotka – Volterra Systems with Solutions in Terms of Lambert’s (W) Function","authors":"Peter H. van der Kamp,&nbsp;David I. McLaren,&nbsp;G. R. W. Quispel","doi":"10.1134/S1560354724580032","DOIUrl":"10.1134/S1560354724580032","url":null,"abstract":"<div><p>We study a class of integrable inhomogeneous Lotka – Volterra systems whose quadratic terms are defined by an antisymmetric matrix and whose linear terms consist of three blocks. We provide the Poisson algebra of their Darboux polynomials and prove a contraction theorem. We then use these results to classify the systems according to the number of functionally independent (and, for some, commuting) integrals. We also establish separability/solvability by quadratures, given the solutions to the 2- and 3-dimensional systems, which we provide in terms of the Lambert <span>(W)</span> function.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 3","pages":"382 - 407"},"PeriodicalIF":0.8,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166837","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
Higher Symmetries of Lattices in 3D 三维网格的更高对称性
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-12-03 DOI: 10.1134/S1560354724060017
Ismagil T. Habibullin, Aigul R. Khakimova
{"title":"Higher Symmetries of Lattices in 3D","authors":"Ismagil T. Habibullin,&nbsp;Aigul R. Khakimova","doi":"10.1134/S1560354724060017","DOIUrl":"10.1134/S1560354724060017","url":null,"abstract":"<div><p>It is known that there is a duality between the Davey – Stewartson type coupled systems and a class of integrable two-dimensional Toda type lattices. More precisely, the coupled systems are generalized symmetries for the lattices and the lattices can be interpreted as dressing chains for the systems. In our recent study we have found a novel lattice which is apparently not related to the known ones by Miura type transformation. In this article we describe higher symmetries to this lattice and derive a new coupled system of DS type.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 6","pages":"853 - 865"},"PeriodicalIF":0.8,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761936","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
Rotations and Integrability 旋转和可积性
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-12-03 DOI: 10.1134/S1560354724060029
Andrey V. Tsiganov
{"title":"Rotations and Integrability","authors":"Andrey V. Tsiganov","doi":"10.1134/S1560354724060029","DOIUrl":"10.1134/S1560354724060029","url":null,"abstract":"<div><p>We discuss some families of integrable and superintegrable systems in <span>(n)</span>-dimensional Euclidean space which are invariant under <span>(mgeqslant n-2)</span> rotations. The invariant Hamiltonian <span>(H=sum p_{i}^{2}+V(q))</span> is integrable with <span>(n-2)</span> integrals of motion <span>(M_{alpha})</span> and an additional integral of\u0000motion <span>(G)</span>, which are first- and fourth-order polynomials in momenta, respectively.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 6","pages":"913 - 930"},"PeriodicalIF":0.8,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1560354724060029.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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