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Regular and Chaotic Dynamics最新文献

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Lagrangian Manifolds in the Theory of Wave Beams and Solutions of the Helmholtz Equation 波束理论中的拉格朗日流形和亥姆霍兹方程的解
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-11-14 DOI: 10.1134/S1560354724570048
Anna V. Tsvetkova
{"title":"Lagrangian Manifolds in the Theory of Wave Beams and Solutions of the Helmholtz Equation","authors":"Anna V. Tsvetkova","doi":"10.1134/S1560354724570048","DOIUrl":"10.1134/S1560354724570048","url":null,"abstract":"<div><p>This paper describes an approach to constructing the asymptotics of Gaussian beams, based on the theory of the canonical Maslov operator and the study of the dynamics and singularities of the corresponding Lagrangian manifolds in the phase space. As an example, we construct global asymptotics of Laguerre – Gauss beams, which are solutions of the Helmholtz equation in the paraxial approximation. Depending on the type of the beam and the emerging singularity on the Lagrangian manifold, asymptotics are expressed in terms of the Airy function or the Bessel function. One of the advantages of the described approach is that we can abandon the paraxial approximation and construct global asymptotics in terms of special functions also for solutions of the original Helmholtz equation, which is illustrated by an example.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 6","pages":"866 - 885"},"PeriodicalIF":0.8,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761995","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 by an External Periodic Force in Ensembles of Globally Coupled Phase Oscillators 全局耦合相位振荡器系综中外部周期力的同步
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-11-14 DOI: 10.1134/S1560354724570012
Semyon S. Abramov, Maxim I. Bolotov, Lev A. Smirnov
{"title":"Synchronization by an External Periodic Force in Ensembles of Globally Coupled Phase Oscillators","authors":"Semyon S. Abramov,&nbsp;Maxim I. Bolotov,&nbsp;Lev A. Smirnov","doi":"10.1134/S1560354724570012","DOIUrl":"10.1134/S1560354724570012","url":null,"abstract":"<div><p>We consider the effect of an external periodic force on chimera states in the phase oscillator model proposed in [Phys. Rev. Lett, v. 101, 00319007 (2008)].\u0000Using the Ott – Antonsen reduction, the dynamical equations for the global order parameter\u0000characterizing the degree of synchronization are constructed. The frequency locking by an external periodic force region is\u0000constructed. The possibility of stable chimeras synchronization and unstable chimeras\u0000stabilization is established. The instability development of the chimera states leads to the appearance of breather chimeras or complete synchronization.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 6","pages":"901 - 912"},"PeriodicalIF":0.8,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761997","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
Switching Activity in an Ensemble of Excitable Neurons 可兴奋神经元集合中的转换活动
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-11-14 DOI: 10.1134/S1560354724570036
Alexander G. Korotkov, Sergey Yu. Zagrebin, Elena Yu. Kadina, Grigory V. Osipov
{"title":"Switching Activity in an Ensemble of Excitable Neurons","authors":"Alexander G. Korotkov,&nbsp;Sergey Yu. Zagrebin,&nbsp;Elena Yu. Kadina,&nbsp;Grigory V. Osipov","doi":"10.1134/S1560354724570036","DOIUrl":"10.1134/S1560354724570036","url":null,"abstract":"<div><p>In [1], a stable heteroclinic cycle was proposed as a mathematical image of switching activity. Due to the stability of the heteroclinic cycle, the sequential activity of the elements of such a network is not limited in time. In this paper, it is proposed to use an unstable heteroclinic cycle as a mathematical image of switching activity. We propose two dynamical systems based on the generalized Lotka – Volterra model of three excitable elements interacting through excitatory couplings. It is shown that in the space of coupling parameters there is a region such that, when coupling parameters in this region are chosen, the phase space of systems contains unstable heteroclinic cycles containing three or six saddles and heteroclinic trajectories connecting them.\u0000Depending on the initial conditions, the phase trajectory will sequentially visit the\u0000neighborhood of saddle equilibria (possibly more than once). The described behavior is\u0000proposed to be used to simulate time-limited switching activity in neural ensembles.\u0000Different transients are determined by different initial conditions. The passage of the\u0000phase point of the system near the saddle equilibria included in the heteroclinic cycle is\u0000proposed to be interpreted as activation of the corresponding element.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 6","pages":"886 - 900"},"PeriodicalIF":0.8,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761996","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
Routes to Chaos in a Three-Dimensional Cancer Model 三维癌症模型中的混沌之路
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-10-02 DOI: 10.1134/S1560354724050010
Efrosiniia Karatetskaia, Vladislav Koryakin, Konstantin Soldatkin, Alexey Kazakov
{"title":"Routes to Chaos in a Three-Dimensional Cancer Model","authors":"Efrosiniia Karatetskaia,&nbsp;Vladislav Koryakin,&nbsp;Konstantin Soldatkin,&nbsp;Alexey Kazakov","doi":"10.1134/S1560354724050010","DOIUrl":"10.1134/S1560354724050010","url":null,"abstract":"<div><p>We provide a detailed bifurcation analysis in a three-dimensional system describing interaction between tumor cells, healthy tissue cells, and cells of the immune system. As is well known from previous studies, the most interesting dynamical regimes in this model are associated with the spiral chaos arising due to the Shilnikov homoclinic loop to a saddle-focus equilibrium [1, 2, 3]. We explain how this equilibrium appears and how it gives rise to Shilnikov attractors.\u0000The main part of this work is devoted to the study of codimension-two bifurcations which,\u0000as we show, are the organizing centers in the system. In particular, we describe bifurcation\u0000unfoldings for an equilibrium state when: (1) it has a pair of zero eigenvalues\u0000(Bogdanov – Takens bifurcation) and (2) zero and a pair of purely imaginary eigenvalues\u0000(zero-Hopf bifurcation). It is shown how these bifurcations are related to the emergence\u0000of the observed chaotic attractors.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 5","pages":"777 - 793"},"PeriodicalIF":0.8,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409509","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 Isolated Periodic Points of Diffeomorphisms with Expanding Attractors of Codimension 1 论具有标度为 1 的扩展吸引子的衍射的孤立周期点
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-10-02 DOI: 10.1134/S1560354724050022
Marina K. Barinova
{"title":"On Isolated Periodic Points of Diffeomorphisms with Expanding Attractors of Codimension 1","authors":"Marina K. Barinova","doi":"10.1134/S1560354724050022","DOIUrl":"10.1134/S1560354724050022","url":null,"abstract":"<div><p>In this paper we consider an <span>(Omega)</span>-stable 3-diffeomorphism whose chain-recurrent set consists of isolated periodic points and hyperbolic 2-dimensional nontrivial attractors. Nontrivial attractors in this case can only be expanding, orientable or not. The most known example from the class under consideration is the DA-diffeomorphism obtained from the algebraic Anosov diffeomorphism, given on a 3-torus, by Smale’s surgery. Each such attractor has bunches of degree 1 and 2. We estimate the minimum number of isolated periodic points using information about the structure of attractors. Also, we investigate the topological structure of ambient manifolds for diffeomorphisms with k bunches and k isolated periodic points.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 5","pages":"794 - 802"},"PeriodicalIF":0.8,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409517","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
Invariant Measures as Obstructions to Attractors in Dynamical Systems and Their Role in Nonholonomic Mechanics 作为动力系统吸引子障碍的不变量及其在非整体力学中的作用
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-09-05 DOI: 10.1134/S156035472456003X
Luis C. García-Naranjo, Rafael Ortega, Antonio J. Ureña
{"title":"Invariant Measures as Obstructions to Attractors in Dynamical Systems and Their Role in Nonholonomic Mechanics","authors":"Luis C. García-Naranjo,&nbsp;Rafael Ortega,&nbsp;Antonio J. Ureña","doi":"10.1134/S156035472456003X","DOIUrl":"10.1134/S156035472456003X","url":null,"abstract":"<div><p>We present some results on the absence of a wide class of invariant measures for dynamical systems possessing attractors.\u0000We then consider a generalization of the classical nonholonomic Suslov problem which shows how previous investigations of existence of\u0000invariant measures for nonholonomic\u0000systems should necessarily be extended beyond the class of measures with strictly positive <span>(C^{1})</span> densities\u0000if one wishes to determine dynamical obstructions to the presence of attractors.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 5","pages":"751 - 763"},"PeriodicalIF":0.8,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196718","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
Phase Portraits of the Equation (ddot{x}+axdot{x}+bx^{3}=0) 方程的相位图 $$ddot{x}+axdot{x}+bx^{3}=0$$
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-09-05 DOI: 10.1134/S1560354724560053
Jaume Llibre, Claudia Valls
{"title":"Phase Portraits of the Equation (ddot{x}+axdot{x}+bx^{3}=0)","authors":"Jaume Llibre,&nbsp;Claudia Valls","doi":"10.1134/S1560354724560053","DOIUrl":"10.1134/S1560354724560053","url":null,"abstract":"<div><p>The second-order differential equation <span>(ddot{x}+axdot{x}+bx^{3}=0)</span> with <span>(a,binmathbb{R})</span> has been studied by several authors mainly due to its applications. Here, for the first time, we classify all its phase portraits according to its parameters <span>(a)</span> and <span>(b)</span>. This classification is done in the Poincaré disc in order to control the orbits that escape or come from infinity. We prove that there are exactly six topologically different phase portraits in the Poincaré disc of the first-order differential system associated to the second-order differential equation. Additionally, we show that this system is always integrable, providing explicitly its first integrals.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 6","pages":"825 - 837"},"PeriodicalIF":0.8,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196720","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
Integral Formulas for the Painlevé-2 Transcendent Painlevé-2 超越积分公式
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-09-05 DOI: 10.1134/S1560354724560041
Oleg M. Kiselev
{"title":"Integral Formulas for the Painlevé-2 Transcendent","authors":"Oleg M. Kiselev","doi":"10.1134/S1560354724560041","DOIUrl":"10.1134/S1560354724560041","url":null,"abstract":"<div><p>In the work we use integral formulas for calculating the monodromy data for the Painlevé-2 equation. The perturbation theory for the auxiliary linear system is constructed and formulas for the variation of the monodromy data are obtained. We also derive a formula for solving the linearized Painlevé-2 equation based on the Fourier-type integral of the squared solutions of the auxiliary linear system of equations.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 6","pages":"838 - 852"},"PeriodicalIF":0.8,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196721","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
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
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