一种新型混沌产生器

A new type of chaotic generator

通过构造一个转折点值α可变的三分段线性奇函数 ,研究一种新型混沌产生器 .这种混沌产生器的主要特征是 ,随着转折点值α在 0 <α≤ 1范围内变化时 ,系统从倍周期分岔进入混沌状态 ,可产生双层单螺旋、单层单螺旋、双层双螺旋和单层双螺旋四种不同类型的混沌吸引子 ,其中双层单螺旋和双层双螺旋为本电路实验中所发现的两类新型混沌吸引子 .分析了这种混沌产生器随α值在 0 <α≤ 1范围内变化时的分岔图、李雅普诺夫指数谱、最大李雅普诺夫指数λmax以及单层双螺旋和双层双螺旋的功率谱 .在此基础上设计硬件电路 ,进行了计算机模拟和电路实验 。

A new type of chaotic generator is studied by constructing a three-segment piecewise-linear odd function with variable breakpoint α . The characteristic of the chaotic generator presented is that when the breakpoint α varies in the range of 0< α ≤1, there is a route to chaos through period-doubling bifurcations,and the double- layer single spiral,single-layer single spiral,double-layer double spiral and single-layer double spiral chaotic attractors can be generated. In particular,the double- layer single spiral and double-layer double spiral are found in our circuit experiment for the first time so far as we know. The bifurcation diagram,Lyapunov exponents λ 1,λ 2,λ 3 ,maximal Lyapunov exponent λ max and the spectrum of the single-layer double spiral and double-layer double spiral are also investigated. The associated electronic circuit is designed and the experimental result is given,which is verified by computer simulation and circuit experiment.