一种新型混沌系统及其电路实验的研究

A new type of chaotic system and its circuit experiment

通过构造只含一个参数的分段函数,研究一种新型混沌系统,其主要特征是随着参数α的变化,系统可产生单层双螺旋,三层双螺旋,双层双螺旋,三层单螺旋,双层单螺旋,单层单螺旋六种不同的混沌吸引子,其中三层双螺旋,二层单螺旋是本电路实验中所发现的两类新的混沌吸引子,并分析该混沌系统随着参数变化的分叉图,最大李雅普诺夫指数谱以及三层双螺旋和三层单螺旋功率谱,最后进行该新型混沌系统的电路实验研究,给出理论分析和实验结果。

A new type of chaotic system is studied by constructing a segment function with only one parameter. The characteristic of the chaotic system presented is that when the parameter at varies, there are the single-layer double spiral, the three-layer double spiral, the double-layer double spiral, the three-layer single spiral, the double-layer single spiral, the single-layer single spiral to be generated. In particular, the three-layer double spiral and the three-layer single spiral chaotic attractors are found in our circuit experiment for the first time so far as we know. The bifurcation diagram of the chaotic system with the parameter α, maximal Lyapunov exponent and the spectrum of the three-layer double spiral and three-layer single spiral are investigated, and then, the associated circuit is designed and the experimental result is given, which is verified by computer simulation and circuit experiment.