受控Rabinovich系统的超混沌系统.pdf

28 11 Vol. 28 No. 11 2011 11 Control Theory Applications Nov. 2011 :2011 Rabinovich (, 537000) : Rabinovich, , . , Lyapunov, . . Rabinovich , . : Rabinovich; ; ; : O175; O29 : A Hyperchaotic system from controlled Rabinovich system LIU Yong-jian (Department of Mathematics and Computation Science, Yulin Normal University, Yulin Guangxi 537000, China) Abstract: A new four-dimensional continuous autonomous hyperchaotic system is presented, which is constructed by adding a linear controller to the famous three-dimensional Rabinovich system. Some basic dynamical behaviors of the hyperchaotic system are further investigated. The corresponding bounded hyperchaotic and chaotic attractor are first nu- merically verified through investigating phase trajectories, Lyapunove exponents, bifurcation path and the analysis of power spectrum and Poincarprojections. Furthermore, the global exponential attractive set and positive invariant set are found for the four-dimensional Rabinovich system; and the strict mathematical proofs are given. Moreover, it is implemented in an electronic circuit and tested experimentally in our laboratory, showing very good agreement between experimental results with the simulation results and validating this new four-dimensional chaotic and hyperchaotic system. Key words: Rabinovich system; hyperchaos; globally exponential attractive set; hyperchaotic circuit 1 (Introduction) [12] Lyapu- . , nov, , [13, 14]. [1] , , . , , , , .