Constructive proof of Lagrange stability and sufficient – Necessary conditions of Lyapunov stability for Yang–Chen chaotic system

Xiaoxin Liao, Guopeng Zhou, Qigui Yang, Yuli Fu and Guanrong Chen

Applied Mathematics and Computation, 2017, vol. 309, issue C, 205-221

Abstract: This paper studies the stability problem of Yang–Chen system. By introducing different radial unbounded Lyapunov functions in different regions, global exponential attractive set of Yang–Chen chaotic system is constructed with geometrical and algebraic methods. Then, simple algebraic sufficient and necessary conditions of global exponential stability, global asymptotic stability, and exponential instability of equilibrium are proposed. And the relevant expression of corresponding parameters for local exponential stability, local asymptotic stability, exponential instability of equilibria are obtained. Furthermore, the branch problem of the system is discussed, some branch expressions are given for the parameters of the system.

Keywords: Yang–Chen system; Lagrange stability; Global exponential attractive set; Lyapunov stability; Branch (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:309:y:2017:i:c:p:205-221

DOI: 10.1016/j.amc.2017.03.033

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