Chaotic ranges of a unified chaotic system and its chaos for five periodic switch cases

Abstract

In this paper, a unified chaotic system is studied in detail. Non-chaotic ranges within alpha is an element of [0,1] are found, where a is the constant parameter of the system. Chaotic range longer than alpha is an element of [0,1], alpha is an element of [-0.015, 1.152], is discovered, which is the extended chaotic range of unified chaotic system. Next, its chaos behaviors for five continuous periodic switch cases, k sin(2) omega T, m sin omega t, 0 similar to 1 triangular wave, -1 similar to 1 triangular wave, and 0 similar to 1 sawtooth wave, are presented. (c) 2006 Elsevier Ltd. All rights reserved.