Antimonotonicity, chaos and multidirectional scroll attractor in autonomous ODEs chaotic system

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Abstract

Three-dimensional autonomous ordinary differential equations (ODEs) are the simplest and most important chaotic systems in nonlinear dynamics. In fact, they have been applied in many fields. In this paper, a systematic methodology for analyzing complex behavior of the ODEs chaotic system, as one of the ODEs chaotic systems, the improved TCS which satisfies the condition a12a21 = 0, is proposed. It is dissipative, chaos, symmetric, antimonotonicity and can generate multiple directional (M× N× L) scroll attractors. Then, bifurcation diagrams, Lyapunov exponents, time series, Poincare sections, and Hausdroff dimensions are analyzed by setting the parameters and initial value. More interestingly, antimonotonicity (named reverse period-doubling bifurcation) and coexisting bifurcations are also reported. Finally, the results of theoretical analyses may be verified by electric experimental.

Original languageEnglish
Article number9072387
Pages (from-to)77171-77178
Number of pages8
JournalIEEE Access
Volume8
DOIs
Publication statusPublished - 2020

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