Analysis and control of multiple chaotic attractors from a three-dimensional system

Xiaoyun Zhong, Minfang Peng, Chi Tse, Shangjiang Guo and Mohammad Shahidehpour

Applied Mathematics and Computation, 2015, vol. 268, issue C, 138-150

Abstract: This paper studies a three-dimensional multiple chaotic system with three quadratic nonlinear terms. The system is shown to exhibit multiple periodic attractors and multiple chaotic attractors including a four-scroll chaotic attractor. It is shown analytically and numerically that any neighborhood of the four-scroll chaotic attractor contains repelling sets with positive Lebesgue measures. Moreover, in terms of incommensurate fractional order systems, a simple fractional differentiator-based controller is designed to suppress chaos. Some basic dynamical behaviors of the system are investigated through analytical techniques and numerical simulation.

Keywords: Chaotic system; Lyapunov exponents; Multiple attractors; Basin of attraction; Chaos control; Fractional-order controller (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:268:y:2015:i:c:p:138-150

DOI: 10.1016/j.amc.2015.06.057

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