A new type of chaotic generator

Abstract

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.