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Dynamics of a generalized Lorenz-like chaos dynamical systems
Fuchen Zhang,Ping Zhou,Jin Qin,Chunlai Mu,Fei Xu
Keywords:Lyapunov exponents; Lyapunov-like function; global stability; global attractivity
Abstract:
      In this work, a new seven-parameter Lorenz-like chaotic system is presented and discussed by combining nonlinear dynamical systems theory with computer simulation. The existence of the ultimate bound set and global exponential attractive set of this chaotic system is proved by using Lyapunov’s direct method. A family of analytic mathematical expression of the ultimate bound sets and global exponential attractive sets involving two parameters are obtained, respectively. Meanwhile, the volumes of the ultimate bound set and global exponential attractive set are obtained, respectively. Numerical simulations are conducted which validates the correctness of the proposed theoretical analysis.