一个新超混沌Lorenz系统的Hopf分岔及电路实现

Hopf Bifurcation and Circuit Implementation of A New Hyperchaotic Lorenz System

对Lorenz系统反馈控制并结合Lyapunov指数方法,提出一个新超混沌Lorenz系统.分析该系统平衡点的稳定性及Hopf分岔的存在性.利用第一Lyapunov系数法给出系统Hopf分岔周期解的稳定性条件.通过数值仿真验证理论分析的正确性,并构建该超混沌Lorenz系统的仿真电路,示波器显示出与数值仿真完全一致的混沌吸引子,从而验证电路设计的正确性和电路实现的可行性.

Firstly,a new hyperchaotic Lorenz system is put forward by feedback control for Lorenz system and the Lyapunov index method.The stability of equilibrium points and the existence of Hopf bifurcation are analyzed in the system.Then the stability condition of Hopf bifurcation periodic solution for the system is given by the first Lyapunov coefficient method.Finally,the correctness of the theoretical analysis is verified by the numerical simulations,and a circuit of the new hyperchaotic Lorenz system is built.The chaotic attractors which display on oscilloscope are of the same with the numerical simulations,so the correctness of the circuit design and the feasibility of circuit implementation are illustrated.