Cross-diffusion induced Turing patterns in a sex-structured predator-prey model

J. Liu, H. Zhou, Lai Zhang

    Research output: Contribution to journalJournal articlepeer-review


    In this paper, we consider a sex-structured predator-prey model with strongly coupled nonlinear reaction diffusion. Using the Lyapunov functional and Leray-Schauder degree theory, the existence and stability of both homogenous and heterogenous steady-states are investigated. Our results demonstrate that the unique homogenous steady-state is locally asymptotically stable for the associated ODE system and PDE system with self-diffusion. With the presence of the cross-diffusion, the homogeneous equilibrium is destabilized, and a heterogenous steady-state emerges as a consequence. In addition, the conditions guaranteeing the emergence of Turing patterns are derived.
    Original languageEnglish
    JournalInternational Journal of Biomathematics
    Issue number4
    Number of pages23
    Publication statusPublished - 2012


    • Predator-prey model
    • Cross-diffusion
    • Turing pattern
    • Sex structure


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