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

IF 2.7 3区 数学 Q1 MATHEMATICS, APPLIED
Xiaoting Lu, Qigui Yang
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引用次数: 0

摘要

本文致力于揭示具有唯一 Lyapunov 稳定均衡的三维 Jerk 系统的隐性吸引子的生成机制。根据偏差曲率张量,确定了具有 Lyapunov 稳定但 Jacobi 不稳定均衡的双参数区域。在这些区域内,系统动力学从 Lyapunov 稳定但 Jacobi 不稳定平衡过渡到隐含周期吸引子,再过渡到隐含混沌吸引子,其对应的 Hamilton 能量分别趋向于恒定、规则和不规则振荡。分析了雅可比不稳定平衡系统在一个参数变化下通向隐性吸引子的路径。结果表明,系统最初经历了次临界霍普夫分岔,形成了一个莱普诺夫不稳定极限周期,随后又经历了极限周期的鞍节点分岔,最终通过费根鲍姆周期加倍路线进入隐性混沌吸引子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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.
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来源期刊
Physica D: Nonlinear Phenomena
Physica D: Nonlinear Phenomena 物理-物理:数学物理
CiteScore
7.30
自引率
7.50%
发文量
213
审稿时长
65 days
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.
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