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Regular and Chaotic Dynamics最新文献

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On Smoothness of Invariant Foliations Near a Homoclinic Bifurcation Creating Lorenz-Like Attractors 关于产生类洛伦兹吸引子的同斜分岔附近不变叶的光滑性
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-02-18 DOI: 10.1134/S1560354725010034
Mikhail I. Malkin, Klim A. Safonov
{"title":"On Smoothness of Invariant Foliations Near a Homoclinic Bifurcation Creating Lorenz-Like Attractors","authors":"Mikhail I. Malkin,&nbsp;Klim A. Safonov","doi":"10.1134/S1560354725010034","DOIUrl":"10.1134/S1560354725010034","url":null,"abstract":"<div><p>This paper deals with the problem of smoothness of the stable invariant foliation for a homoclinic bifurcation with a neutral saddle in symmetric systems of differential equations. We give an\u0000improved sufficient condition for the existence of an invariant smooth foliation on a cross-section transversal to the stable manifold of the saddle. It is shown that the smoothness of the invariant foliation depends on the gap between the leading stable eigenvalue of the saddle and other stable eigenvalues. We also obtain an equation to describe the one-dimensional factor map, and we study the renormalization properties of this map. The improved information on the smoothness of the foliation and the factor map allows one to extend Shilnikov’s results on the birth of Lorenz attractors under the bifurcation considered.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 1","pages":"26 - 44"},"PeriodicalIF":0.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145122074","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
Chain-Recurrent (C^{0})- (Omega)-Blowup in (C^{1})-Smooth Simplest Skew Products on Multidimensional Cells 链-循环(C^{0}) - (Omega) - (C^{1})中的放大-多维单元上的光滑最简单的倾斜产品
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-02-18 DOI: 10.1134/S156035472501006X
Lyudmila S. Efremova, Dmitry A. Novozhilov
{"title":"Chain-Recurrent (C^{0})- (Omega)-Blowup in (C^{1})-Smooth Simplest Skew Products on Multidimensional Cells","authors":"Lyudmila S. Efremova,&nbsp;Dmitry A. Novozhilov","doi":"10.1134/S156035472501006X","DOIUrl":"10.1134/S156035472501006X","url":null,"abstract":"<div><p>In this paper we prove criteria of a <span>(C^{0})</span>- <span>(Omega)</span>-blowup in <span>(C^{1})</span>-smooth skew products with a\u0000closed set of periodic points on multidimensional cells and give examples of maps that admit such a <span>(Omega)</span>-blowup.\u0000Our method is based on the study of the properties of the set of chain-recurrent points. We also\u0000prove that the set of weakly nonwandering points of maps under consideration coincides with\u0000the chain-recurrent set, investigate the approximation (in the <span>(C^{0})</span>-norm) and entropy properties\u0000of <span>(C^{1})</span>-smooth skew products with a closed set of periodic points.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 1","pages":"120 - 140"},"PeriodicalIF":0.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145122055","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
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
Dynamics of an Elliptic Foil with an Attached Vortex in an Ideal Fluid: The Integrable Case 理想流体中附涡椭圆箔的动力学：可积情况
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-12-27 DOI: 10.1134/S1560354724590015
Alexander A. Kilin, Anna M. Gavrilova, Elizaveta M. Artemova
{"title":"Dynamics of an Elliptic Foil with an Attached Vortex in an Ideal Fluid: The Integrable Case","authors":"Alexander A. Kilin,&nbsp;Anna M. Gavrilova,&nbsp;Elizaveta M. Artemova","doi":"10.1134/S1560354724590015","DOIUrl":"10.1134/S1560354724590015","url":null,"abstract":"<div><p>This paper is concerned with the plane-parallel\u0000motion of an elliptic foil with an attached vortex of\u0000constant strength in an ideal fluid.\u0000Special attention is given to the case in which the vortex\u0000lies on the continuation of one of the semiaxes of the ellipse. It is shown\u0000that in this case there exist no attracting solutions and\u0000the system is integrable by the Euler – Jacobi theorem.\u0000A complete qualitative analysis of the equations of\u0000motion is carried out for cases where the vortex lies on the continuation of\u0000the large or the small semiaxis of the ellipse.\u0000Possible types of trajectories of an elliptic foil with an attached\u0000vortex are established: quasi-periodic, unbounded\u0000(going to infinity) and periodic trajectories.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"931 - 951"},"PeriodicalIF":0.8,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145646274","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
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