简化Lorenz系统多翅膀混沌吸引子的设计与电路实现

基于简化Lorenz系统,通过设计非线性函数,得到单方向多翅膀混沌吸引子.在此基础上,通过引入切换控制函数,得到了网格多翅膀混沌吸引子.通过相图、耗散性、平衡点、分岔图和Poincaré截面方法,分析了系统的动力学特性.结果表明,该多翅膀系统具有丰富的动力学行为.设计并实现了网格多翅膀系统的模拟电路,通过示波器观测到网格多翅膀混沌吸引子,验证了该系统的物理可实现性,电路实验结果与数值仿真结果相一致.

Design and circuit implementation of the simplified Lorenz multi wing chaotic attractor

N-wing attractors were first obtained by introducing a nonlinear function on the simplified Lorenz system in this paper. The grid multi wing attractors were then realized through switching the control function in the z direction. Moreover, the dynamical characteristics of the Lorenz system were studied by the attractor phase diagram, dissipation, equilibrium points, bifurcation diagram and Poincaré section. The results show that the simplified Lorenz system exhibited a rich dynamical behaviors. Finally, the analog circuit of the system was designed and developed. The grid multi wing attractors were observed through the oscilloscope, and the physical implementation of chaotic circuit was verified. It is found that the results of circuit experiment and numerical simulation were accordant.