受控Rabinovich系统的超混沌系统

Hyperchaotic system from controlled Rabinovich system

在三维Rabinovich系统的基础上,通过引入一个线性状态反馈控制器构建一个新的四维超混沌系统,分析其基本动力学行为.在保证系统有界的前提下,通过计算Lyapunov指数值和研究其分岔的途径,证实其超混沌的特性.还给出了四维超混沌系统的指数吸引域和正向不变集等.同时也设计了实现四维Rabinovich超混沌吸引子的实际电路,验证了理论分析的结果.

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 Poincaré projections.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.