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Regular and Chaotic Dynamics最新文献

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Mechanism of Selectivity in the Coupled FitzHugh – Nagumo Neurons 菲茨休--南云耦合神经元的选择性机制
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-09-05 DOI: 10.1134/S1560354724560016
Andrei V. Bukh, Elena V. Rybalova, Igor A. Shepelev, Tatiyana E. Vadivasova
{"title":"Mechanism of Selectivity in the Coupled FitzHugh – Nagumo Neurons","authors":"Andrei V. Bukh,&nbsp;Elena V. Rybalova,&nbsp;Igor A. Shepelev,&nbsp;Tatiyana E. Vadivasova","doi":"10.1134/S1560354724560016","DOIUrl":"10.1134/S1560354724560016","url":null,"abstract":"<div><p>We study the spike activity of two mutually coupled FitzHugh – Nagumo neurons, which is influenced by two-frequency signals. The ratio of frequencies in the external signal corresponds to musical intervals (consonances). It has been discovered that this system can exhibit selective properties for identifying musical intervals. The mechanism of selectivity is shown, which is associated with the influence on the spiking frequency of neurons by intensity of the external signal and nature of the interaction of neurons.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 5","pages":"764 - 776"},"PeriodicalIF":0.8,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196719","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
Continuations and Bifurcations of Relative Equilibria for the Positively Curved Three-Body Problem 正曲三体问题相对平衡点的延续和分岔
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-09-05 DOI: 10.1134/S1560354724560028
Toshiaki Fujiwara, Ernesto Pérez-Chavela
{"title":"Continuations and Bifurcations of Relative Equilibria for the Positively Curved Three-Body Problem","authors":"Toshiaki Fujiwara,&nbsp;Ernesto Pérez-Chavela","doi":"10.1134/S1560354724560028","DOIUrl":"10.1134/S1560354724560028","url":null,"abstract":"<div><p>The positively curved three-body problem is a natural extension of the planar Newtonian three-body problem to the sphere\u0000<span>(mathbb{S}^{2})</span>. In this paper we study the extensions of the Euler and Lagrange relative\u0000equilibria (<span>(RE)</span> for short) on the plane to the sphere.</p><p>The <span>(RE)</span> on <span>(mathbb{S}^{2})</span> are not isolated in general.\u0000They usually have one-dimensional continuation in the three-dimensional shape space.\u0000We show that there are two types of bifurcations. One is the bifurcations between\u0000Lagrange <span>(RE)</span> and Euler <span>(RE)</span>. Another one is between the different types of the shapes of Lagrange <span>(RE)</span>. We prove that\u0000bifurcations between equilateral and isosceles Lagrange <span>(RE)</span> exist\u0000for the case of equal masses, and that bifurcations between isosceles and scalene\u0000Lagrange <span>(RE)</span> exist for the partial equal masses case.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 6","pages":"803 - 824"},"PeriodicalIF":0.8,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196722","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-Resonant Conditions for the Klein – Gordon Equation on the Circle 圆上克莱因-戈登方程的非共振条件
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-08-04 DOI: 10.1134/S1560354724040026
Roberto Feola, Jessica Elisa Massetti
{"title":"Non-Resonant Conditions for the Klein – Gordon Equation on the Circle","authors":"Roberto Feola,&nbsp;Jessica Elisa Massetti","doi":"10.1134/S1560354724040026","DOIUrl":"10.1134/S1560354724040026","url":null,"abstract":"<div><p>We consider the infinite-dimensional vector of frequencies <span>(omega(mathtt{m})=(sqrt{j^{2}+mathtt{m}})_{jinmathbb{Z}})</span>, <span>(mathtt{m}in[1,2])</span>\u0000arising from a linear Klein – Gordon equation on the one-dimensional torus and prove that there exists a positive measure set of masses <span>(mathtt{m}^{prime})</span>s for which <span>(omega(mathtt{m}))</span> satisfies a Diophantine condition similar to the one introduced by Bourgain in [14],\u0000in the context of the Schrödinger equation with convolution potential.\u0000The main difficulties we have to deal with are\u0000the asymptotically linear nature of the (infinitely many) <span>(omega_{j}^{prime})</span>s and the degeneracy coming from having only one parameter at disposal for their modulation.\u0000As an application we provide estimates on the inverse of the adjoint action of the associated quadratic Hamiltonian on homogenenous polynomials of any degree in Gevrey category.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Treschev)","pages":"541 - 564"},"PeriodicalIF":0.8,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141935536","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 Elliptic Lower-Dimensional Invariant Tori with Prescribed Frequencies in Hamiltonian Systems with Small Parameters 论小参数哈密顿系统中具有规定频率的椭圆形低维不变矩阵
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-08-04 DOI: 10.1134/S156035472404004X
Hanru Zou, Junxiang Xu
{"title":"On Elliptic Lower-Dimensional Invariant Tori with Prescribed Frequencies in Hamiltonian Systems with Small Parameters","authors":"Hanru Zou,&nbsp;Junxiang Xu","doi":"10.1134/S156035472404004X","DOIUrl":"10.1134/S156035472404004X","url":null,"abstract":"<div><p>In this paper we consider the persistence of elliptic lower-dimensional invariant tori with prescribed frequencies in Hamiltonian systems with small parameters. Under the Brjuno nondegeneracy condition,\u0000if the prescribed frequencies satisfy a Diophantine condition, by the KAM technique we prove that for most of small parameters in the sense of Lebesgue measure, the Hamiltonian systems admit a lower-dimensional\u0000invariant torus whose frequency vector is a dilation of the prescribed frequencies.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Treschev)","pages":"583 - 604"},"PeriodicalIF":0.8,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141935550","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
3D Orbital Architecture of Exoplanetary Systems: KAM-Stability Analysis 系外行星系统的 3D 轨道结构：KAM 稳定性分析
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-08-04 DOI: 10.1134/S1560354724040038
Chiara Caracciolo, Ugo Locatelli, Marco Sansottera, Mara Volpi
{"title":"3D Orbital Architecture of Exoplanetary Systems: KAM-Stability Analysis","authors":"Chiara Caracciolo,&nbsp;Ugo Locatelli,&nbsp;Marco Sansottera,&nbsp;Mara Volpi","doi":"10.1134/S1560354724040038","DOIUrl":"10.1134/S1560354724040038","url":null,"abstract":"<div><p>We study the KAM-stability of several single star two-planet\u0000nonresonant extrasolar systems. It is likely that the observed\u0000exoplanets are the most massive of the system considered. Therefore,\u0000their robust stability is a crucial and necessary condition for the\u0000long-term survival of the system when considering potential\u0000additional exoplanets yet to be seen. Our study is based on the\u0000construction of a combination of lower-dimensional elliptic and KAM\u0000tori, so as to better approximate the dynamics in the framework of\u0000accurate secular models. For each extrasolar system, we explore the\u0000parameter space of both inclinations: the one with respect to the\u0000line of sight and the mutual inclination between the planets. Our\u0000approach shows that remarkable inclinations, resulting in\u0000three-dimensional architectures that are far from being coplanar,\u0000can be compatible with the KAM stability of the system. We find\u0000that the highest values of the mutual inclinations are comparable to\u0000those of the few systems for which the said inclinations are determined\u0000by the observations.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Treschev)","pages":"565 - 582"},"PeriodicalIF":0.8,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1560354724040038.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141935476","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
Persistence of Multiscale Degenerate Invariant Tori in Reversible Systems with Degenerate Frequency Mapping 具有退化频率映射的可逆系统中多尺度退化不变环的持续性
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-08-04 DOI: 10.1134/S1560354724040051
Xiaomei Yang, Junxiang Xu
{"title":"Persistence of Multiscale Degenerate Invariant Tori in Reversible Systems with Degenerate Frequency Mapping","authors":"Xiaomei Yang,&nbsp;Junxiang Xu","doi":"10.1134/S1560354724040051","DOIUrl":"10.1134/S1560354724040051","url":null,"abstract":"<div><p>This paper considers a class of nearly integrable reversible systems\u0000whose unperturbed part has a degenerate frequency mapping and a degenerate equilibrium point.\u0000Based on some KAM techniques\u0000and the topological degree theory, we prove the persistence of multiscale degenerate hyperbolic lower-dimensional invariant tori with prescribed frequencies.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Treschev)","pages":"605 - 619"},"PeriodicalIF":0.8,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141935478","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
Erratum to: Isolated Diophantine Numbers 勘误：孤立二阶数
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-07-17 DOI: 10.1134/S1560354724550033
Fernando Argentieri, Luigi Chierchia
{"title":"Erratum to: Isolated Diophantine Numbers","authors":"Fernando Argentieri,&nbsp;Luigi Chierchia","doi":"10.1134/S1560354724550033","DOIUrl":"10.1134/S1560354724550033","url":null,"abstract":"","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Treschev)","pages":"716 - 716"},"PeriodicalIF":0.8,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1560354724550033.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412182","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
Isolated Diophantine Numbers 孤立二阶数
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-07-05 DOI: 10.1134/S156035472455001X
Fernando Argentieri, Luigi Chierchia
{"title":"Isolated Diophantine Numbers","authors":"Fernando Argentieri,&nbsp;Luigi Chierchia","doi":"10.1134/S156035472455001X","DOIUrl":"10.1134/S156035472455001X","url":null,"abstract":"<div><p>In this note, we discuss the topology of Diophantine numbers, giving simple explicit\u0000examples of Diophantine isolated numbers (among those with the same Diophantine constants),\u0000showing that <i>Diophantine sets are not always Cantor sets</i>.</p><p>General properties of isolated Diophantine numbers are also briefly discussed.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Treschev)","pages":"536 - 540"},"PeriodicalIF":0.8,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S156035472455001X.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576048","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
Nineteen Fifty-Four: Kolmogorov’s New “Metrical Approach” to Hamiltonian Dynamics 19 54：科尔莫戈罗夫的汉密尔顿动力学新 "韵律方法
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-07-05 DOI: 10.1134/S1560354724550021
Luigi Chierchia, Isabella Fascitiello
{"title":"Nineteen Fifty-Four: Kolmogorov’s New “Metrical Approach” to Hamiltonian Dynamics","authors":"Luigi Chierchia,&nbsp;Isabella Fascitiello","doi":"10.1134/S1560354724550021","DOIUrl":"10.1134/S1560354724550021","url":null,"abstract":"<div><p>We review Kolmogorov’s 1954 fundamental paper <i>On the persistence of conditionally periodic motions under a small change in the Hamilton function</i> (Dokl. akad. nauk SSSR, 1954, vol. <b>98</b>, pp. 527–530), both from the historical and the mathematical point of view.\u0000In particular, we discuss Theorem 2 (which deals with the measure in phase space of persistent tori), the proof of which is not discussed at all by Kolmogorov, notwithstanding its centrality in his program in classical mechanics.</p><p>In Appendix, an interview (May 28, 2021) to Ya. Sinai on Kolmogorov’s legacy in classical mechanics is reported.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Treschev)","pages":"517 - 535"},"PeriodicalIF":0.8,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141578145","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
KAM for Vortex Patches 用于涡流补丁的 KAM
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-06-21 DOI: 10.1134/S1560354724540013
Massimiliano Berti
{"title":"KAM for Vortex Patches","authors":"Massimiliano Berti","doi":"10.1134/S1560354724540013","DOIUrl":"10.1134/S1560354724540013","url":null,"abstract":"<div><p>In the last years substantial mathematical progress has been made in KAM theory\u0000for <i>quasi-linear</i>/fully nonlinear\u0000Hamiltonian partial differential equations, notably for\u0000water waves and Euler equations.\u0000In this survey we focus on recent advances in quasi-periodic vortex patch\u0000solutions of the <span>(2d)</span>-Euler equation in <span>(mathbb{R}^{2})</span>\u0000close to uniformly rotating Kirchhoff elliptical vortices,\u0000with aspect ratios belonging to a set of asymptotically full Lebesgue measure.\u0000The problem is reformulated into a quasi-linear Hamiltonian equation for a radial displacement from the ellipse. A major difficulty of the KAM proof is the presence of a zero normal mode frequency, which is due to the conservation of the angular momentum. The key novelty to overcome this degeneracy is to perform a perturbative symplectic reduction of the angular momentum, introducing it as a symplectic variable in the spirit of the Darboux – Carathéodory theorem of symplectic rectification, valid in finite dimension.\u0000This approach is particularly delicate in an infinite-dimensional phase space: our symplectic\u0000change of variables is a nonlinear modification of the transport flow generated by the angular\u0000momentum itself.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Treschev)","pages":"654 - 676"},"PeriodicalIF":0.8,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501790","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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