Jacobi Stability of Simple Chaotic Systems with One Lyapunov Stable Equilibrium
Jacobi Stability of Simple Chaotic Systems with One Lyapunov Stable Equilibrium
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DOI：
10.1115/1.4050954
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发表时间：
2021-07
影响因子：
2
通讯作者：
Changzhi Li;Biyue Chen;Aimin Liu;Huanhuan Tian
中科院分区：
文献类型：
--
作者：
Changzhi Li;Biyue Chen;Aimin Liu;Huanhuan Tian
本文利用KCC理论对23个只有一个Lyapunov稳定平衡点的简单混沌系统进行了Jacobi稳定性分析，并从几何角度分析了这些系统的混沌行为。与李雅普诺夫稳定不同，每个系统的唯一平衡总是雅可比不稳定的。此外，讨论了这23个系统在平衡附近的偏离矢量的动力学行为，揭示了它们的混沌起始点，并进一步从几何上证明了每个系统的唯一Lyapunov稳定平衡和混沌吸引子的共存。得到的结果表明，这些混沌系统对平衡的小扰动不具有鲁棒性，表明系统对内部环境极为敏感。这表明由这些系统产生的混沌流可能与平衡的雅可比不稳定性有关。希望本文的研究有助于揭示隐藏混沌吸引子的真实几何结构。
This paper presents Jacobi stability analysis of 23 simple chaotic systems with only one Lyapunov stable equilibrium by Kosambi-Cartan-Chern (KCC) theory, and analyzes the chaotic behavior of these systems from the geometric viewpoint. Different from Lyapunov stability, the unique equilibrium for each system is always Jacobi unstable. Moreover, the dynamical behaviors of deviation vector near equilibrium are discussed to reveal the onset of chaos for these 23 systems, and show furtherly the coexistence of unique Lyapunov stable equilibrium and chaotic attractor for each system geometrically. The obtaining results show that these chaotic systems are not robust to small perturbations of the equilibrium, indicating that the systems are extremely sensitive to internal environment. This reveals that the chaotic flows generated by these systems may be related to Jacobi instability of the equilibrium. It is hoped that the study of this paper can help reveal the true geometrical structure of hidden chaotic attractors.