A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family

作者：Yu, P^*; Liao, X X; Xie, S L; Fu, Y L

来源：Communications in Nonlinear Science & Numerical Simulation, 2009, 14(7): 2886-2896.

DOI：10.1016/j.cnsns.2008.10.008

• General Lorenz family
• Globally exponentially attractive set
• Positive invariant set
• Generalized Lyapunov function
• Ultimate boundedness of chaotic system

In this paper, we give a constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family, which contains four independent parameters and is more general than any Lorenz systems studied so far in the literature. The system considered in this paper not only contains the classical Lorenz system and the generalized Lorenz family as special cases, but also provides three new Lorenz systems, which do not belong to the generalized Lorenz system, but the general Lorenz system. The results presented in this paper contain all the existing relative results as special cases.

• 出版日期2009-7
• 单位华南理工大学; 华中科技大学