Some New Results for the Generalized Lorenz System

Fuchen Zhang ^[1] ; Xiaofeng Liao ^[2] ; Guangyun Zhang ^[1]
1. [1] Chongqing Technology and Business University
  
  Chongqing Technology and Business University
  
  China
2. [2] Southwest University
  
  Southwest University
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 16, Nº 3, 2017, págs. 749-759
Idioma: inglés
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Resumen
- The bound of a chaotic dynamical system is important for chaos control, chaos synchronization, estimating the dimensions of chaotic attractors, and other engineering applications. It is a difficult work to get the bounds of a chaotic dynamical system. This paper further studies the bounds of the generalized Lorenz system (2) for a11 < 0, a22 > 0, λ3 < 0 based on Lyapunov stability theory. To the best of our knowledge, it is a very difficult task to study the bounds of the system (2) for a11 < 0, a22 > 0, λ3 < 0 and there are few papers to study the bounds of chaotic systems for this case.