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Regular and Chaotic Dynamics最新文献

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On Bifurcations of Symmetric Elliptic Orbits 论对称椭圆轨道的分岔
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010039
Marina S. Gonchenko
{"title":"On Bifurcations of Symmetric Elliptic Orbits","authors":"Marina S. Gonchenko","doi":"10.1134/S1560354724010039","DOIUrl":"10.1134/S1560354724010039","url":null,"abstract":"<div><p>We study bifurcations of symmetric elliptic fixed points in the case of <i>p</i>:<i>q</i> resonances with odd <span>(qgeqslant 3)</span>. We consider the case where the initial area-preserving map <span>(bar{z}=lambda z+Q(z,z^{*}))</span> possesses the central symmetry, i. e., is invariant under the change of variables <span>(zto-z)</span>, <span>(z^{*}to-z^{*})</span>. We construct normal forms for such maps in the case <span>(lambda=e^{i2pifrac{p}{q}})</span>, where <span>(p)</span> and <span>(q)</span> are mutually prime integer numbers, <span>(pleqslant q)</span> and <span>(q)</span> is odd, and study local bifurcations of the fixed point <span>(z=0)</span> in various settings. We prove the appearance of garlands consisting of four <span>(q)</span>-periodic orbits, two orbits are elliptic and two orbits are saddles, and describe the corresponding bifurcation diagrams for one- and two-parameter families. We also consider the case where the initial map is reversible and find conditions where nonsymmetric periodic orbits of the garlands are nonconservative (contain symmetric pairs of stable and unstable orbits as well as area-contracting and area-expanding saddles).</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"25 - 39"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099146","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 in Coupled Heteroclinic Cycles Between Weak Chimeras 弱嵌合体之间耦合异次元循环中的混沌现象
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010131
Artyom E. Emelin, Evgeny A. Grines, Tatiana A. Levanova
{"title":"Chaos in Coupled Heteroclinic Cycles Between Weak Chimeras","authors":"Artyom E. Emelin,&nbsp;Evgeny A. Grines,&nbsp;Tatiana A. Levanova","doi":"10.1134/S1560354724010131","DOIUrl":"10.1134/S1560354724010131","url":null,"abstract":"<div><p>Heteroclinic cycles are widely used in neuroscience in order to mathematically describe different mechanisms of functioning of the brain and nervous system. Heteroclinic cycles and interactions between them can be a source of different types of nontrivial dynamics. For instance, as it was shown earlier, chaotic dynamics can appear as a result of interaction via diffusive couplings between two stable heteroclinic cycles between saddle equilibria. We go beyond these findings by considering two coupled stable heteroclinic cycles rotating in opposite\u0000directions between weak chimeras. Such an ensemble can be mathematically described by a system of six phase equations. Using two-parameter bifurcation analysis, we investigate the scenarios of\u0000emergence and destruction of chaotic dynamics in the system under study.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"205 - 217"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099420","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
IN HONOR OF SERGEY GONCHENKO AND VLADIMIR BELYKH 纪念谢尔盖-冈琴科和弗拉基米尔-别列赫
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010015
Nikita Barabash, Igor Belykh, Alexey Kazakov, Michael Malkin, Vladimir Nekorkin, Dmitry Turaev
{"title":"IN HONOR OF SERGEY GONCHENKO AND VLADIMIR BELYKH","authors":"Nikita Barabash,&nbsp;Igor Belykh,&nbsp;Alexey Kazakov,&nbsp;Michael Malkin,&nbsp;Vladimir Nekorkin,&nbsp;Dmitry Turaev","doi":"10.1134/S1560354724010015","DOIUrl":"10.1134/S1560354724010015","url":null,"abstract":"","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"1 - 5"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140516195","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 a Pendulum in a Rarefied Flow 稀薄流中摆的动力学特性
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010088
Alexey Davydov, Alexander Plakhov
{"title":"Dynamics of a Pendulum in a Rarefied Flow","authors":"Alexey Davydov,&nbsp;Alexander Plakhov","doi":"10.1134/S1560354724010088","DOIUrl":"10.1134/S1560354724010088","url":null,"abstract":"<div><p>We consider the dynamics of a rod on the plane in a flow of non-interacting point particles moving at a fixed speed. When colliding with the rod, the particles are reflected elastically and then leave the plane of motion of the rod and do not interact with it. A thin unbending weightless “knitting needle” is fastened to the\u0000massive rod. The needle is attached to an anchor point and can rotate freely about it. The particles do not interact with the needle.</p><p>The equations of dynamics are obtained, which are piecewise analytic: the phase space is divided into four regions where the analytic formulas are different. There are two fixed points of the system, corresponding to the position of the rod parallel to the flow velocity, with the anchor point at the front and the back. It is found that the former point is topologically a stable focus, and the latter is topologically a saddle. A qualitative description of the phase portrait of the system is obtained.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"134 - 142"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140098986","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
Numerical Study of Discrete Lorenz-Like Attractors 离散类洛伦兹吸引力的数值研究
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010064
Alexey Kazakov, Ainoa Murillo, Arturo Vieiro, Kirill Zaichikov
{"title":"Numerical Study of Discrete Lorenz-Like Attractors","authors":"Alexey Kazakov,&nbsp;Ainoa Murillo,&nbsp;Arturo Vieiro,&nbsp;Kirill Zaichikov","doi":"10.1134/S1560354724010064","DOIUrl":"10.1134/S1560354724010064","url":null,"abstract":"<div><p>We consider a homotopic to the identity family of maps, obtained as a discretization of the Lorenz system, such that the dynamics of the last is recovered as a limit dynamics when the discretization parameter tends to zero. We investigate the structure of the discrete Lorenz-like attractors that the map shows for different values of parameters. In particular, we check the pseudohyperbolicity of the observed discrete attractors and show how to\u0000use interpolating vector fields to compute kneading diagrams for near-identity maps. For larger discretization parameter values, the map exhibits what appears to be genuinely-discrete Lorenz-like attractors, that is, discrete chaotic pseudohyperbolic attractors with a negative second Lyapunov exponent. The numerical methods used are general enough to be adapted for arbitrary near-identity discrete systems with similar phase space structure.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"78 - 99"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099185","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
Twin Heteroclinic Connections of Reversible Systems 可逆系统的双异次元连接
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010040
Nikolay E. Kulagin, Lev M. Lerman, Konstantin N. Trifonov
{"title":"Twin Heteroclinic Connections of Reversible Systems","authors":"Nikolay E. Kulagin,&nbsp;Lev M. Lerman,&nbsp;Konstantin N. Trifonov","doi":"10.1134/S1560354724010040","DOIUrl":"10.1134/S1560354724010040","url":null,"abstract":"<div><p>We examine smooth four-dimensional vector fields reversible under some\u0000smooth involution <span>(L)</span> that has a smooth two-dimensional submanifold of fixed\u0000points. Our main interest here is in the orbit structure of such a system\u0000near two types of heteroclinic connections involving saddle-foci and\u0000heteroclinic orbits connecting them. In both cases we found families of\u0000symmetric periodic orbits, multi-round heteroclinic connections and\u0000countable families of homoclinic orbits of saddle-foci. All this suggests that the orbit\u0000structure near such connections is very complicated. A non-variational version of the stationary Swift – Hohenberg equation is considered, as an example, where such structure has been found numerically.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"40 - 64"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099145","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 Homeomorphisms of Three-Dimensional Manifolds with Pseudo-Anosov Attractors and Repellers 论具有伪阿诺索夫吸引子和排斥子的三维流形的同构性
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010106
Vyacheslav Z. Grines, Olga V. Pochinka, Ekaterina E. Chilina
{"title":"On Homeomorphisms of Three-Dimensional Manifolds with Pseudo-Anosov Attractors and Repellers","authors":"Vyacheslav Z. Grines,&nbsp;Olga V. Pochinka,&nbsp;Ekaterina E. Chilina","doi":"10.1134/S1560354724010106","DOIUrl":"10.1134/S1560354724010106","url":null,"abstract":"<div><p>The present paper is devoted to a study of orientation-preserving homeomorphisms on three-dimensional manifolds with a non-wandering set consisting of a finite number of surface attractors and repellers. The main results of the paper relate to a class of homeomorphisms for which the restriction of the map to a connected component of the non-wandering set is topologically conjugate to an orientation-preserving pseudo-Anosov homeomorphism. The ambient <span>(Omega)</span>-conjugacy of a homeomorphism from the class with a locally direct product of a pseudo-Anosov homeomorphism and a rough transformation of the circle is proved. In addition, we prove that the centralizer of a pseudo-Anosov homeomorphisms consists of only pseudo-Anosov and periodic maps.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"156 - 173"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099200","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 Regularity of Invariant Foliations 论不变叶形的规律性
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010027
Dmitry Turaev
{"title":"On the Regularity of Invariant Foliations","authors":"Dmitry Turaev","doi":"10.1134/S1560354724010027","DOIUrl":"10.1134/S1560354724010027","url":null,"abstract":"<div><p>We show that the stable invariant foliation of codimension 1 near a zero-dimensional hyperbolic set of a <span>(C^{beta})</span> map with <span>(beta&gt;1)</span> is <span>(C^{1+varepsilon})</span> with some <span>(varepsilon&gt;0)</span>. The result is applied to the restriction of higher regularity\u0000maps to normally hyperbolic manifolds. An application to the theory of the Newhouse phenomenon is discussed.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"6 - 24"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140098869","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
Asymptotics of Self-Oscillations in Chains of Systems of Nonlinear Equations 非线性方程系统链中自振荡的渐近性
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010143
Sergey A. Kashchenko
{"title":"Asymptotics of Self-Oscillations in Chains of Systems of Nonlinear Equations","authors":"Sergey A. Kashchenko","doi":"10.1134/S1560354724010143","DOIUrl":"10.1134/S1560354724010143","url":null,"abstract":"<div><p>We study the local dynamics of chains of coupled nonlinear systems of second-order ordinary differential equations of diffusion-difference type. The main assumption is that the number of elements of chains is large enough. This condition allows us to pass to the problem with a continuous spatial variable.\u0000Critical cases have been considered while studying the stability of the equilibrum state.\u0000It is shown that all these cases have infinite dimension. The research technique is based on the development and application of special methods for construction of normal forms.\u0000Among the main results of the paper, we include the creation of new nonlinear boundary value problems of parabolic type, whose nonlocal dynamics describes the local behavior of solutions of the original system.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"218 - 240"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099152","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
Quasi-Periodicity at Transition from Spiking to Bursting in the Pernarowski Model of Pancreatic Beta Cells 胰腺β细胞的 Pernarowski 模型中从尖峰到爆发的准周期性转变
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010076
Haniyeh Fallah, Andrey L. Shilnikov
{"title":"Quasi-Periodicity at Transition from Spiking to Bursting in the Pernarowski Model of Pancreatic Beta Cells","authors":"Haniyeh Fallah,&nbsp;Andrey L. Shilnikov","doi":"10.1134/S1560354724010076","DOIUrl":"10.1134/S1560354724010076","url":null,"abstract":"<div><p>This paper studies quasi-periodicity phenomena appearing at the transition from spiking to bursting activities in the Pernarowski model of pancreatic beta cells. Continuing the parameter, we show that the torus bifurcation is responsible for the transition between spiking and bursting. Our investigation involves different torus bifurcations, such as supercritical torus bifurcation, saddle torus canard, resonant torus, self-similar torus fractals, and torus destruction. These bifurcations give rise to complex or multistable dynamics. Despite being a dissipative system, the model still exhibits KAM tori, as we have illustrated. We provide two scenarios for the onset of resonant tori using the Poincaré return map, where global bifurcations happen because of the saddle-node or inverse period-doubling bifurcations. The blue-sky catastrophe takes place at the transition route from bursting to spiking.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"100 - 119"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099144","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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