具有隐藏吸引子的单涡卷混沌系统与电路实验

Single scroll chaotic system with hidden attractor and its circuit implementation

本文通过构建系统模型,增加控制参数和改变非线性项以及增加常数项相结合的方法构造出一类单涡卷混沌系统,并探究其中两种典型混沌系统的复杂特性。首先,分析该两种包含隐藏吸引子混沌系统的数值仿真相图、时域波形图、Poincare截面图和功率谱图。其次,讨论不同系统参数改变时,Lyapunov指数谱和分岔图在整个系统中的变化趋势,并从中发现多种隐藏吸引子的共存现象。最后,搭建实物硬件电路图,在示波器上得到混沌吸引子,其与Matlab仿真结果相一致,验证了混沌电路的实际可操作性。

This paper constructs a single-scroll chaotic system by constructing a system model,adding control parameters,changing nonlinear terms,adding constant terms,and explores the complex characteristics of the chaotic system.Firstly,the two kinds of chaotic systems with hidden attractor are numerically analyzed with phase diagram,time domain waveform,Poincare section and power spectrum.Secondly,the changing trend of Lyapunov exponent spectrum and bifurcation diagram in the whole system is discussed when the different system parameters have been changed,and the coexistence phenomenon of multiple hidden attractors has been found.Finally,we build the hardware circuit diagram,and the corresponding chaotic attractors are obtained on the oscilloscope.Compared with the Matlab simulation results,the actual operability of the chaotic circuit is proved.