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

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

6 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)138-150
Number of pages13
JournalApplied Mathematics and Computation
Volume268
DOIs
Publication statusPublished - 13 Jul 2015

Keywords

  • Basin of attraction
  • Chaos control
  • Chaotic system
  • Fractional-order controller
  • Lyapunov exponents
  • Multiple attractors

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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