Dynamic analysis, circuit realization, control design and image encryption application of an extended Lü system with coexisting attractors

Qiang Lai, Benyamin Norouzi, Feng Liu

    Research output: Contribution to journalArticlepeer-review

    154 Scopus citations

    Abstract

    This paper introduces an extended Lü system with coexisting attractors. The number and stability of equilibria are determined. The coexisting attractors of the system are displayed by the bifurcation diagrams, Lyapunov exponent spectrum, phase portraits. It is shown that the system has a pair of strange attractors, a pair of limit cycles, a pair of point attractors for different initial conditions. The circuit implementation of the chaotic attractor and coexisting attractors of the system are presented. The control problem of the system is studied as well. A controller is designed to stabilize the system to the origin and realize the switching between two chaotic attractors based on the passive control method. Moreover, a chaotic image encryption algorithm is proposed according to the system. The performance of the algorithm is numerically analyzed.

    Original languageEnglish
    Pages (from-to)230-245
    Number of pages16
    JournalChaos, Solitons and Fractals
    Volume114
    DOIs
    StatePublished - Sep 2018

    Keywords

    • An extended Lü system
    • Bifurcation diagram
    • Coexisting attractors
    • Equilibrium
    • Image encryption
    • Initial value
    • Passive control

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