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 α ∈ [0, 1] are found, where α is the constant parameter of the system. Chaotic range longer than α ∈ [0, 1], α ∈ [−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 sin2 ωT, m sin ωt, 0 ∼ 1 triangular wave, −1 ∼ 1 triangular wave, and 0 ∼ 1 sawtooth wave, are presented.

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