一种新型混沌产生器

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λ_max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 关键词： 混沌产生器 双层双螺旋 双层单螺旋 电路实验

A new type of chaotic generator

A new type of chaotic generator is studied by constructing a three_segment piec ewise_linear odd function with variable breakpoint α. The characteristic of the chaotic generator presented is that when the breakpoint α varies in th e range of 0<α≤1, there is a route to chaos through period_doubling bifurcations, and the doubl e_ 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 b ifurca tion diagram, Lyap unov 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 ver ified by computer simulation and circuit experiment.