{"title":"具有唯一李雅普诺夫稳定均衡的三维 Jerk 系统中的雅可比稳定性、汉密尔顿能量和通向隐藏吸引子的路径","authors":"Xiaoting Lu, Qigui Yang","doi":"10.1016/j.physd.2024.134423","DOIUrl":null,"url":null,"abstract":"<div><div>This paper is devoted to reveal the generation mechanism of hidden attractors of the 3D Jerk systems with unique Lyapunov stable equilibrium. In the light of the deviation curvature tensor, the two-parameter regions with Lyapunov stable but Jacobi unstable equilibrium are identified. Within these regions, the system’s dynamics transition from Lyapunov stable but Jacobi unstable equilibrium to hidden periodic and then to hidden chaotic attractors, which the corresponding Hamilton energy tend to be constant, regular and irregular oscillations, respectively. The route to hidden attractors of the systems with Jacobi unstable equilibrium is analyzed under one parameter variation. The results show that the systems initially undergo a subcritical Hopf bifurcation, resulting in a Lyapunov unstable limit cycle, followed by a saddle–node bifurcation of limit cycle, ultimately entering hidden chaotic attractors via the Feigenbaum period-doubling route.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134423"},"PeriodicalIF":2.7000,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Jacobi stability, Hamilton energy and the route to hidden attractors in the 3D Jerk systems with unique Lyapunov stable equilibrium\",\"authors\":\"Xiaoting Lu, Qigui Yang\",\"doi\":\"10.1016/j.physd.2024.134423\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This paper is devoted to reveal the generation mechanism of hidden attractors of the 3D Jerk systems with unique Lyapunov stable equilibrium. In the light of the deviation curvature tensor, the two-parameter regions with Lyapunov stable but Jacobi unstable equilibrium are identified. Within these regions, the system’s dynamics transition from Lyapunov stable but Jacobi unstable equilibrium to hidden periodic and then to hidden chaotic attractors, which the corresponding Hamilton energy tend to be constant, regular and irregular oscillations, respectively. The route to hidden attractors of the systems with Jacobi unstable equilibrium is analyzed under one parameter variation. The results show that the systems initially undergo a subcritical Hopf bifurcation, resulting in a Lyapunov unstable limit cycle, followed by a saddle–node bifurcation of limit cycle, ultimately entering hidden chaotic attractors via the Feigenbaum period-doubling route.</div></div>\",\"PeriodicalId\":20050,\"journal\":{\"name\":\"Physica D: Nonlinear Phenomena\",\"volume\":\"470 \",\"pages\":\"Article 134423\"},\"PeriodicalIF\":2.7000,\"publicationDate\":\"2024-11-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physica D: Nonlinear Phenomena\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167278924003737\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278924003737","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Jacobi stability, Hamilton energy and the route to hidden attractors in the 3D Jerk systems with unique Lyapunov stable equilibrium
This paper is devoted to reveal the generation mechanism of hidden attractors of the 3D Jerk systems with unique Lyapunov stable equilibrium. In the light of the deviation curvature tensor, the two-parameter regions with Lyapunov stable but Jacobi unstable equilibrium are identified. Within these regions, the system’s dynamics transition from Lyapunov stable but Jacobi unstable equilibrium to hidden periodic and then to hidden chaotic attractors, which the corresponding Hamilton energy tend to be constant, regular and irregular oscillations, respectively. The route to hidden attractors of the systems with Jacobi unstable equilibrium is analyzed under one parameter variation. The results show that the systems initially undergo a subcritical Hopf bifurcation, resulting in a Lyapunov unstable limit cycle, followed by a saddle–node bifurcation of limit cycle, ultimately entering hidden chaotic attractors via the Feigenbaum period-doubling route.
期刊介绍:
Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.