Chaotic behaviour of nonlinear coupled reaction-diffusion system in four-dimensional space

Li Zhang, Shutang Liu, Chenglong Yu

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    Abstract

    In recent years, nonlinear coupled reaction-diffusion (CRD) system has been widely investigated by coupled map lattice method. Previously, nonlinear behaviour was observed dynamically when one or two of the three variables in the discrete system change. In this paper, we consider the chaotic behaviour when three variables change, which is called as four-dimensional chaos. When two parameters in the discrete system are unknown, we first give the existing condition of the chaos in four-dimensional space by the generalized definitions of spatial periodic orbits and spatial chaos. In addition, the chaotic behaviour will vary with the parameters. Then we propose a generalized Lyapunov exponent in four-dimensional space to characterize the different effects of parameters on the chaotic behaviour, which has not been studied in detail. In order to verify the chaotic behaviour of the system and the different effects clearly, we simulate the dynamical behaviour in two-and three-dimensional spaces.

    Original languageEnglish
    Pages (from-to)995-1009
    Number of pages15
    JournalPramana-Journal of Physics
    Volume82
    Issue number6
    DOIs
    Publication statusPublished - Jun 2014

    Keywords

    • Chaos
    • Coupled map lattice
    • Higher dimension
    • Partial differential equation

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