Regular and Chaotic Dynamics最新文献

{"title":"Verification of Chaos in a Human Cardiovascular System Model","authors":"Pavel V. Kuptsov,&nbsp;Yuriy M. Ishbulatov,&nbsp;Anatoly S. Karavaev,&nbsp;Nataliya V. Stankevich","doi":"10.1134/S1560354725020078","DOIUrl":"10.1134/S1560354725020078","url":null,"abstract":"<div><p>This study discusses an approach for estimation of the largest Lyapunov exponent for the mathematical model of the cardiovascular system. The accuracy was verified using the confidence intervals approach. The algorithm was used to investigate the effects of noises with different amplitudes and spectral compositions on the dynamics of the model. Three sets of parameters are considered, corresponding to different states of the human cardiovascular system model. It is shown that, in each case, the model exhibited chaotic dynamics. The model gave different responses to the changes in the characteristics of the noise, when using different sets of parameters. The noise had both constructive and destructive effects, depending on the parameters of the model and the noise, by, respectively, amplifying or inhibiting the chaotic dynamics of the model.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 2","pages":"291 - 305"},"PeriodicalIF":0.8,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793150","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}

{"title":"Scalar Polynomial Vector Fields in Real and Complex Time","authors":"Bernold Fiedler","doi":"10.1134/S1560354725020030","DOIUrl":"10.1134/S1560354725020030","url":null,"abstract":"<div><p>Recent PDE studies address global boundedness versus finite-time blow-up in equations like the quadratic parabolic heat equation versus the nonconservative quadratic Schrödinger equation.\u0000The two equations are related by passage from real to purely imaginary time.\u0000Renewed interest in pioneering work by Masuda, in particular, has further explored the option to\u0000circumnavigate blow-up in real time, by a detour in complex time.</p><p>In the present paper, the simplest scalar ODE case is studied for polynomials\u0000</p><div><div><span>\u0000$$dot{w}=f(w)=(w-e_{0})cdotldotscdot(w-e_{d-1}),$$\u0000</span></div><div>\u0000 (*)\u0000 </div></div><p>\u0000of degree <span>(d)</span> with <span>(d)</span> simple complex zeros.\u0000The explicit solution by separation of variables and explicit integration is an almost trivial matter.</p><p>In a classical spirit, indeed, we describe the complex Riemann surface <span>(mathcal{R})</span> of the global nontrivial solution <span>((w(t),t))</span> in complex time, as an unbranched cover of the punctured Riemann sphere <span>(winwidehat{mathbb{C}}_{d}:=widehat{mathbb{C}}setminus{e_{0},ldots,e_{d-1}})</span> .\u0000The flow property, however, fails at <span>(w=inftyinwidehat{mathbb{C}}_{d})</span>.\u0000The global consequences depend on the period map of the residues <span>(2pimathrm{i}/f^{prime}(e_{j}))</span> of <span>(1/f)</span> at the punctures, in detail.\u0000We therefore show that polynomials <span>(f)</span> exist for arbitrarily prescribed residues with zero sum.\u0000This result is not covered by standard interpolation theory.</p><p>Motivated by the PDE case, we also classify the planar <i>real-time</i> phase portraits of (*).\u0000Here we prefer a Poincaré compactification of <span>(winmathbb{C}=mathbb{R}^{2})</span> by the closed unit disk. This regularizes <span>(w=infty)</span> by <span>(2(d-1))</span> equilibria, alternately stable and unstable within the invariant circle boundary at infinity.\u0000In structurally stable hyperbolic cases of nonvanishing real parts <span>(Re f^{prime}(e_{j})neq 0)</span>, for the linearizations at all equilibria <span>(e_{j})</span>, and in the absence of saddle-saddle heteroclinic orbits, we classify all compactified phase portraits, up to orientation-preserving orbit equivalence and time reversal.\u0000Combinatorially, their source/sink connection graphs correspond to the planar trees of <span>(d)</span> vertices or, dually, the circle diagrams with <span>(d-1)</span> nonintersecting chords.\u0000The correspondence provides an explicit count of the above equivalence classes of ODE (*), in real time.</p><p>We conclude with a discussion of some higher-dimensional problems.\u0000Not least, we offer a 1,000 € reward for the discovery, or refutation, of complex entire homoclinic orbits.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 2","pages":"188 - 225"},"PeriodicalIF":0.8,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793154","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}

{"title":"Singular Points in Generic Two-Parameter Families of Vector Fields on a 2-Manifold","authors":"Dmitry A. Filimonov,&nbsp;Yulij S. Ilyashenko","doi":"10.1134/S1560354725020066","DOIUrl":"10.1134/S1560354725020066","url":null,"abstract":"<div><p>In this paper, we give a full description of all possible singular points that occur in generic 2-parameter families of vector fields on compact 2-manifolds. This is a part of a large project aimed at a complete study of global bifurcations in two-parameter families of vector fields on the two-sphere.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 2","pages":"279 - 290"},"PeriodicalIF":0.8,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793151","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}

{"title":"A Geometric Model for Pseudohyperbolic Shilnikov Attractors","authors":"Dmitry Turaev","doi":"10.1134/S1560354725020029","DOIUrl":"10.1134/S1560354725020029","url":null,"abstract":"<div><p>We describe a <span>(C^{1})</span>-open set of systems of differential equations in <span>(R^{n})</span>, for any <span>(ngeqslant 4)</span>, where every system has a chain-transitive chaotic attractor which\u0000contains a saddle-focus equilibrium with a two-dimensional unstable manifold. The attractor also includes a wild hyperbolic set and a heterodimensional cycle involving\u0000hyperbolic sets with different numbers of positive Lyapunov exponents.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 2","pages":"174 - 187"},"PeriodicalIF":0.8,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1560354725020029.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793153","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}

{"title":"Topological Classification of Polar Flows on Four-Dimensional Manifolds","authors":"Elena Ya. Gurevich,&nbsp;Ilya A. Saraev","doi":"10.1134/S1560354725020054","DOIUrl":"10.1134/S1560354725020054","url":null,"abstract":"<div><p>S. Smale has shown that any closed smooth manifold admits a gradient-like flow, which is a structurally stable flow with a finite nonwandering set. Polar flows form a subclass of gradient-like flows characterized by the simplest nonwandering set for the given manifold, consisting of exactly one source, one sink, and a finite number of saddle equilibria. We describe the topology of four-dimensional closed manifolds that admit polar flows without heteroclinic intersections, as well as all classes of topological equivalence of polar flows on each manifold. In particular, we demonstrate that there exists a countable set of nonequivalent flows with a given number <span>(kgeqslant 2)</span> of saddle equilibria on each manifold, which contrasts with the situation in lower-dimensional analogues.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 2","pages":"254 - 278"},"PeriodicalIF":0.8,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793157","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}

{"title":"On Morse – Smale 3-Diffeomorphisms with a Given Tuple of Sink Points Periods","authors":"Marina K. Barinova,&nbsp;Evgenii M. Osenkov,&nbsp;Olga V. Pochinka","doi":"10.1134/S1560354725020042","DOIUrl":"10.1134/S1560354725020042","url":null,"abstract":"<div><p>In investigating dynamical systems with chaotic attractors, many aspects of global behavior of a flow or a diffeomorphism with such an attractor are studied by replacing a nontrivial attractor by a trivial one [1, 2, 11, 14].\u0000Such a method allows one to reduce the original system to a regular system, for instance, of a Morse – Smale system, matched with it. In most cases, the possibility of such a substitution is justified by the existence of Morse – Smale diffeomorphisms with partially determined periodic data, the complete understanding of their dynamics and the topology of manifolds, on which they are defined. With this aim in mind, we consider Morse – Smale diffeomorphisms <span>(f)</span> with determined periods of the sink points, given on a closed smooth 3-manifold. We have shown that, if the total number of these sinks is <span>(k)</span>, then their nonwandering set consists of an even number of points which is at least <span>(2k)</span>. We have found necessary and sufficient conditions for the realizability of a set of sink periods in the minimal nonwandering set. We claim that such diffeomorphisms exist only on the 3-sphere and establish for them a sufficient condition for the existence of heteroclinic points. In addition, we prove that the Morse – Smale 3-diffeomorphism with an arbitrary set of sink periods can be implemented in the nonwandering set consisting of <span>(2k+2)</span> points. We claim that any such a diffeomorphism is supported by a lens space or the skew product <span>(mathbb{S}^{2}tilde{times}mathbb{S}^{1})</span>.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 2","pages":"226 - 253"},"PeriodicalIF":0.8,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793156","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}

{"title":"Affine Generalizations of the Nonholonomic Problem of a Convex Body Rolling without Slipping on the Plane","authors":"Mariana Costa-Villegas,&nbsp;Luis C. García-Naranjo","doi":"10.1134/S1560354725510021","DOIUrl":"10.1134/S1560354725510021","url":null,"abstract":"<div><p>We introduce a class of examples which provide an affine generalization of the nonholonomic problem of a convex body that rolls without slipping on the plane. These examples are constructed by taking as given two vector fields, one on the surface of the body and another on the plane, which specify the velocity of the contact point. We investigate dynamical aspects of the system such as existence of first integrals, smooth invariant measure, integrability\u0000and chaotic behavior, giving special attention to special shapes of the convex body and specific choices of the vector fields for which the affine nonholonomic constraints may be physically realized.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 3","pages":"354 - 381"},"PeriodicalIF":0.8,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168001","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}

{"title":"Parametrised KAM Theory, an Overview","authors":"Henk W. Broer,&nbsp;Heinz Hanßmann,&nbsp;Florian Wagener","doi":"10.1134/S156035472551001X","DOIUrl":"10.1134/S156035472551001X","url":null,"abstract":"<div><p>Kolmogorov – Arnold – Moser theory started in the 1950s as the\u0000perturbation theory for persistence of multi- or\u0000quasi-periodic motions in Hamiltonian systems.\u0000Since then the theory obtained a branch where the persistent\u0000occurrence of quasi-periodicity is studied in various\u0000classes of systems, which may depend on parameters.\u0000The view changed into the direction of structural stability,\u0000concerning the occurrence of quasi-periodic tori on a set\u0000of positive Hausdorff measure in a sub-manifold of the\u0000product of phase space and parameter space.\u0000This paper contains an overview of this development with\u0000an emphasis on the world of dissipative systems, where\u0000families of quasi-periodic tori occur and bifurcate in a\u0000persistent way.\u0000The transition from orderly to chaotic dynamics here forms\u0000a leading thought.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 3","pages":"408 - 450"},"PeriodicalIF":0.8,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168002","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}

{"title":"Dynamical Properties of Continuous Semigroup Actions and Their Products","authors":"Mikhail V. Meshcheryakov,&nbsp;Nina I. Zhukova","doi":"10.1134/S1560354725010071","DOIUrl":"10.1134/S1560354725010071","url":null,"abstract":"<div><p>Continuous actions of topological semigroups on products <span>(X)</span> of an arbitrary family of topological spaces <span>(X_{i})</span>, <span>(iin J,)</span> are studied. The relationship between the dynamical properties of semigroups acting on the factors <span>(X_{i})</span> and the same properties of the product of semigroups on the product <span>(X)</span> of these spaces is investigated. We consider the following dynamical properties: topological transitivity, existence of a dense orbit, density of a union of minimal sets, and density of the set of points with closed orbits. The sensitive dependence on initial conditions is investigated for countable products of metric spaces. Various examples are constructed. In particular, on an infinite-dimensional torus we have constructed a continual\u0000family of chaotic semigroup dynamical systems\u0000that are pairwise topologically not conjugate by homeomorphisms preserving the structure of the\u0000product of this torus.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 1","pages":"141 - 154"},"PeriodicalIF":0.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145122056","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}

{"title":"In Honor of the 90th Anniversary of Leonid Pavlovich Shilnikov (1934–2011)","authors":"Sergey Gonchenko,&nbsp;Mikhail Malkin,&nbsp;Dmitry Turaev","doi":"10.1134/S1560354725010010","DOIUrl":"10.1134/S1560354725010010","url":null,"abstract":"","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 1","pages":"1 - 8"},"PeriodicalIF":0.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145122059","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}