An Extremely Simple Chaotic System with Infinitely Many Coexisting Attractors

Qiang Lai, Paul Didier Kamdem Kuate, Feng Liu, Herbert Ho Ching Iu

    Research output: Contribution to journalArticlepeer-review

    151 Scopus citations

    Abstract

    The discovery of simple chaotic systems with complex dynamics has always been an interesting research work. This brief aims to construct an extremely simple chaotic system with infinitely many coexisting chaotic attractors. The system consists of five terms with two nonlinearities, and has an infinite number of unstable equilibria owing to its sinusoidal nonlinearity. The most prominent feature of the system is that it coexists infinitely many chaotic attractors for different initial values and fixed system parameters. To our best knowledge, there is no 3-D system with such a simple mathematical model can produce infinitely many coexisting chaotic attractors. The phenomenon of coexisting attractors of the new system is numerically investigated. The circuit and microcontroller-based implementation of the system are presented as well.

    Original languageEnglish
    Article number8758327
    Pages (from-to)1129-1133
    Number of pages5
    JournalIEEE Transactions on Circuits and Systems II: Express Briefs
    Volume67
    Issue number6
    DOIs
    StatePublished - Jun 2020

    Keywords

    • Chaotic system
    • circuit implementation
    • coexisting attractors
    • initial conditions
    • microcontroller

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