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Regular and Chaotic Dynamics最新文献

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Andronov – Hopf and Andronov – Vitt – Shilnikov Bifurcations as a Route to Complex Dynamics in the Suslov Top Andronov - Hopf和Andronov - Vitt - Shilnikov分岔作为Suslov顶复杂动力学的一条路径
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-10-19 DOI: 10.1134/S1560354726050011
Efrosiniia Karatetskaia, Alexey Kazakov, Vladislav Koryakin, Klim Safonov
{"title":"Andronov – Hopf and Andronov – Vitt – Shilnikov Bifurcations as a Route to Complex Dynamics in the Suslov Top","authors":"Efrosiniia Karatetskaia,&nbsp;Alexey Kazakov,&nbsp;Vladislav Koryakin,&nbsp;Klim Safonov","doi":"10.1134/S1560354726050011","DOIUrl":"10.1134/S1560354726050011","url":null,"abstract":"<div><p>We study the chaotic dynamics of the Suslov top, a classical nonholonomic system. This system possesses a rich bifurcation structure, which we explore numerically via Lyapunov diagrams and bifurcation analysis in a two-parameter plane. This structure is organized by a codimension-2 point where an equilibrium state has eigenvalues <span>((0,iomega,-iomega))</span> and a homoclinic loop. From this point, two important bifurcation curves originate: the Andronov – Hopf bifurcation curve, corresponding to the birth of a stable periodic orbit from an equilibrium state, and the Andronov – Vitt – Shilnikov bifurcation curve, corresponding to the birth of a stable periodic orbit from a homoclinic loop of a saddle-node equilibrium. We show how chaotic attractors and repellers emerge from equilibrium states, grow, and merge into mixed dynamics. We also discuss the connection of this organizing codimension-2 point with the blue sky catastrophe phenomenon: the birth of a stable periodic orbit of infinite period and length.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"669 - 690"},"PeriodicalIF":0.8,"publicationDate":"2026-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149214559","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
Poincaré Second Species Solutions of the General Three-Body Problem 一般三体问题的第二种解
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-10-19 DOI: 10.1134/S1560354726050059
Sergey V. Bolotin
{"title":"Poincaré Second Species Solutions of the General Three-Body Problem","authors":"Sergey V. Bolotin","doi":"10.1134/S1560354726050059","DOIUrl":"10.1134/S1560354726050059","url":null,"abstract":"<div><p>We consider the plane three-body problem with two of the masses much smaller than the third.\u0000Periodic solutions with near collisions of the small bodies were named\u0000by Poincaré <i>second species solutions</i>.\u0000Poincaré gave an idea of how to prove their existence, but didn’t provide an actual proof.\u0000Complete proofs appeared much later and only for the restricted three-body problem.\u0000We reduce the problem of second species solutions of the general three-body problem\u0000to the study of dynamics of a billiard type problem and show how to transform\u0000the arguments of Poincaré into a rigorous proof.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"738 - 750"},"PeriodicalIF":0.8,"publicationDate":"2026-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149214560","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
Robust Stabilization of Periodic Orbits for a Spherical Robot via Servoconstraints 基于伺服约束的球面机器人周期轨道鲁棒镇定
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-10-19 DOI: 10.1134/S1560354726050096
Oleg Yu. Sumenkov, Sergei V. Gusev
{"title":"Robust Stabilization of Periodic Orbits for a Spherical Robot via Servoconstraints","authors":"Oleg Yu. Sumenkov,&nbsp;Sergei V. Gusev","doi":"10.1134/S1560354726050096","DOIUrl":"10.1134/S1560354726050096","url":null,"abstract":"<div><p>This paper treats the problem of finding feasible periodic motions and that of their robust orbital stabilization\u0000for a spherical robot. The first problem is tackled using the servoconstraint\u0000approach based on the mathematical model of a pendulum-type spherical robot moving on\u0000a plane under the no-slip and no-loss-of-contact assumptions. The second problem is addressed through a generalization of\u0000the well-known\u0000Andronov – Vitt theorem, specifically by introducing the transverse coordinates of co-dimension\u0000one that are zero on a desired orbit. Linearizing the dynamics in the transverse coordinates\u0000results in a linear system with periodic coefficients (LSPC).\u0000A rigorous procedure is suggested for stabilizing the LSPC in the presence of structured\u0000uncertainties and matched disturbances using vector relay control. This control strategy\u0000forces the LSPC solutions onto a predefined time-periodic family of subspaces, where the\u0000exponential stability is ensured.\u0000The effectiveness of the overall framework is demonstrated through simulations.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"825 - 842"},"PeriodicalIF":0.8,"publicationDate":"2026-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149214558","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
Nonsmooth Multipattern Burster: a New Approach to Solvable Piecewise-Smooth Modelingof Neuron Activity 非光滑多模式爆发：神经元活动可解分段光滑建模的新方法
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-10-19 DOI: 10.1134/S1560354726050023
Nikita V. Barabash, Maria V. Suntsova, Vladimir N. Belykh
{"title":"Nonsmooth Multipattern Burster: a New Approach to Solvable Piecewise-Smooth Modeling\u0000of Neuron Activity","authors":"Nikita V. Barabash,&nbsp;Maria V. Suntsova,&nbsp;Vladimir N. Belykh","doi":"10.1134/S1560354726050023","DOIUrl":"10.1134/S1560354726050023","url":null,"abstract":"<div><p>In this paper, we constructed a new model of the neuron membrane potential in the form of a piecewise-smooth (PWS) slow-fast system.\u0000Its fast part is a two-dimensional PWS subsystem specially “sewn” from the normal forms of\u0000a stable focus and a saddle-node bifurcation, and the slow one-dimensional equation serves to\u0000periodically force the fast one.\u0000Our approach to constructing PWS systems in this way allows them to qualitatively reproduce the phase space structure of their smooth counterpart and also provide explicit solutions.\u0000By obtaining an exact Poincaré map as a composition of solutions and examining it, we proved the complete bifurcation structure of the fast subsystem.\u0000By selecting three bifurcation routes and applying a time-periodic change of the subsystem parameter along them using the third slow equation, we obtained three different types of bursting patterns.\u0000Finally, we showed that, when coupled into a network, our PWS models form a synthetic central pattern generator that manifests a traveling bursting wave.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"691 - 709"},"PeriodicalIF":0.8,"publicationDate":"2026-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149214580","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
Wavelet-Based Detection of Strange Nonchaotic Attractors 基于小波的奇异非混沌吸引子检测
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-10-19 DOI: 10.1134/S1560354726050084
Dmitry Lubchenko
{"title":"Wavelet-Based Detection of Strange Nonchaotic Attractors","authors":"Dmitry Lubchenko","doi":"10.1134/S1560354726050084","DOIUrl":"10.1134/S1560354726050084","url":null,"abstract":"<div><p>Strange nonchaotic attractors (SNA) are fractal invariant sets characterized by aperiodic dynamics and nonpositive largest Lyapunov exponents. Due to the fractal geometry and the absence of exponential sensitivity to initial conditions, SNA are often difficult to distinguish from chaotic attractors using time-series data. This study examines the applicability of wavelet-based analysis for the detection of strange nonchaotic regimes in dynamical systems. The proposed approach involves the analysis of wavelet scalograms and global wavelet energy spectra. It is shown that quasiperiodic and strange regimes can be distinguished by the structure of their scalograms. To distinguish between strange nonchaotic and chaotic regimes, global wavelet energy spectra are employed. Numerical results demonstrate the applicability of this method for identifying quasiperiodic, strange nonchaotic, and chaotic regimes from time-series data.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"814 - 824"},"PeriodicalIF":0.8,"publicationDate":"2026-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149214556","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
Modeling of Controlled Omnidirectional Motion of a Spherical Robot with Electromagnetic Drive 电磁驱动球形机器人受控全向运动建模
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-10-19 DOI: 10.1134/S1560354726050060
Dmitry V. Balandin, Alexander M. Tuzikov, Ruslan S. Biryukov
{"title":"Modeling of Controlled Omnidirectional Motion of a Spherical Robot with Electromagnetic Drive","authors":"Dmitry V. Balandin,&nbsp;Alexander M. Tuzikov,&nbsp;Ruslan S. Biryukov","doi":"10.1134/S1560354726050060","DOIUrl":"10.1134/S1560354726050060","url":null,"abstract":"<div><p>This paper extends the modeling and control of a spherical robot with electromagnetic drive (SRED) from planar to fully three-dimensional motion on uneven surfaces. The robot consists of two concentric spherical shells: an outer shell carrying permanent magnets (PMs) and an inner shell with solenoid-type electromagnets (EMs); rolling is produced by the controlled electromagnetic interaction between the two magnet arrays. To enable omnidirectional rolling, the magnet placement is generalized to vertex-transitive polyhedra with cubic or icosahedral symmetry, which preserves the scalarity of the inertia tensors and allows the existing optimal control framework to be applied without modification. Within this class, <span>(M=60)</span> PMs on a rhombicosidodecahedron and <span>(S=24)</span> EMs on a truncated octahedron are selected; numerical evaluation over <span>(10^{4})</span> relative orientations confirms that a nonzero torque can be generated about an arbitrary axis. The drive model is reformulated as a three-dimensional torque map matrix, and coil currents and terminal voltages are recovered from a reference torque via the generalized-<span>(H_{2})</span> optimal controller, a Tikhonov-regularized pseudoinverse, and Kirchhoff’s circuit equations with back-EMF terms. Simulations of straight-line rolling, lateral-offset correction, and three-dimensional path tracking on a Gaussian bell-shaped surface confirm convergence of the tracking error to zero, with currents and voltages within the range of standard low-voltage motor drivers.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"751 - 777"},"PeriodicalIF":0.8,"publicationDate":"2026-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149214510","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
A Neural Network Approach for Generating Libration Point Orbits 一种生成振动点轨道的神经网络方法
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-10-19 DOI: 10.1134/S1560354726050072
Lev Pyatko, Sergey Aksenov
{"title":"A Neural Network Approach for Generating Libration Point Orbits","authors":"Lev Pyatko,&nbsp;Sergey Aksenov","doi":"10.1134/S1560354726050072","DOIUrl":"10.1134/S1560354726050072","url":null,"abstract":"<div><p>In the circular restricted three-body problem, families of periodic and quasi-periodic orbits exist in the vicinity of the libration points and are of significant interest for practical applications. This work presents a neural network-based algorithm for orbit construction and station-keeping, applicable to both periodic and quasi-periodic orbits near collinear libration points. The method employs a fully connected neural network trained on labeled trajectory data and iteratively refined using trajectories generated during previous stages of the algorithm. The proposed approach was applied to orbit generation near the Sun-Earth L1 libration point and demonstrated the ability to generalize to a broader class of trajectories than those included in the training set.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"794 - 813"},"PeriodicalIF":0.8,"publicationDate":"2026-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149214581","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
Combinatorics of Hamiltonian Normal Forms 哈密顿范式的组合学
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-10-19 DOI: 10.1134/S1560354726050035
Dmitry V. Treschev
{"title":"Combinatorics of Hamiltonian Normal Forms","authors":"Dmitry V. Treschev","doi":"10.1134/S1560354726050035","DOIUrl":"10.1134/S1560354726050035","url":null,"abstract":"<div><p>We discuss algebraic and combinatorial aspects of the Hamiltonian normal form theory. The main objective is to describe the normal form near a singular point by an explicit formula in terms of the original Hamiltonian, avoiding the normalization procedure. In the case of one degree of freedom we compute the normal form as an explicit nonlinear functional, applied to the original Hamiltonian. In arbitrary dimension the corresponding formulas are more complicated but still explicit.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"710 - 726"},"PeriodicalIF":0.8,"publicationDate":"2026-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149214557","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 Chaotic Axiom A Diffeomorphisms with Codimension One Saddles and Basic Sets 余维一鞍和基本集的混沌公理A的微分同态
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-10-19 DOI: 10.1134/S1560354726050047
Vladislav S. Medvedev, Evgeny V. Zhuzhoma
{"title":"On Chaotic Axiom A Diffeomorphisms with Codimension One Saddles and Basic Sets","authors":"Vladislav S. Medvedev,&nbsp;Evgeny V. Zhuzhoma","doi":"10.1134/S1560354726050047","DOIUrl":"10.1134/S1560354726050047","url":null,"abstract":"<div><p>We study Axiom A diffeomorphisms (in the sense of Smale) on a closed orientable <span>(n)</span>-manifold <span>(M^{n})</span>, <span>(ngeqslant 4)</span>, whose nonwandering sets consist of codimension one orientable attractors, repellers, and isolated saddle periodic orbits with the same Morse index. Such systems combine chaotic dynamics on basic sets with regular dynamics near trivial periodic orbits. We prove that the supporting manifold <span>(M^{n})</span> is homeomorphic to a connected sum of several copies of the <span>(n)</span>-dimensional torus. Moreover, we obtain a complete classification of such systems up to global conjugacy on their nonwandering sets. The invariant of conjugacy is a finite collection of Anosov automorphisms of the torus, called a <i>tube</i>, defined up to equivalence under linear automorphisms with determinants of the same sign. This extends the classical Plykin – Grines classification of individual codimension one basic sets to systems with multiple coexisting attractors and repellers.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"727 - 737"},"PeriodicalIF":0.8,"publicationDate":"2026-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149214579","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
Decomposition of Symmetrical Classes of Central Configurations 中心构型对称类的分解
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-06-15 DOI: 10.1134/S1560354726520023
Marcelo P. Santos, Leon D. da Silva
{"title":"Decomposition of Symmetrical Classes of Central Configurations","authors":"Marcelo P. Santos,&nbsp;Leon D. da Silva","doi":"10.1134/S1560354726520023","DOIUrl":"10.1134/S1560354726520023","url":null,"abstract":"<div><p>We study central configurations when the set of positions is symmetric. We use a theorem (proved in [33]) that allows us to use the representation theory of finite groups to explore the symmetry properties of equations for central configurations. This approach simplifies equations for central configurations by considering arbitrary numbers of bodies, symmetry groups, and dimensions.\u0000We discuss how to use this theorem to obtain a more refined decomposition of the equations than that given before. The decomposition presented here uses the symmetry-adapted basis method.</p><p>As an application, we give a complete description of the existence and which masses are possible for central configurations of two nested regular\u0000tetrahedra, two nested regular octahedrons, and two nested regular cubes.\u0000To do this, we employ some methods of rational parameterizations and isolation of zeros of multivariate polynomials. The decomposition obtained allows symbolic calculations to be used to study the expressions.\u0000In this way, we summarized the same discussions of works done in [11, 25, 45] and extended\u0000them by completing the discussion on the\u0000cube case, in the inverse and direct problems.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 4","pages":"531 - 559"},"PeriodicalIF":0.8,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613152","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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