Global stability of a stage-structured predator-prey model with prey dispersal

Rui Xu, M. A. J. Chaplain, F. A. Davidson

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    Abstract

    A delayed Lotka–Volterra type predator-prey model with stage structure for predator and prey dispersal in two-patch environments is investigated. It is assumed that immature individuals and mature individuals of predator species are divided by a fixed age, and that immature predators do not feed on prey and do not have the ability to reproduce; on the other hand, it is assumed that the prey species can disperse between one patch with a low level of food and without predation and one patch with a higher level of food but with predation. By means of two different kinds of Lyapunov functionals, sufficient conditions are derived respectively for the global asymptotic stability of a positive equilibrium of the model. By analyzing the characteristic equation, criterion is established for the local stability of the positive equilibrium. Numerical simulations are presented to illustrate our main results.
    Original languageEnglish
    Pages (from-to)293-314
    Number of pages22
    JournalApplied Mathematics and Computation
    Volume171
    Issue number1
    DOIs
    Publication statusPublished - 2005

    Keywords

    • Stage structure
    • Time delay
    • Dispersal
    • Permanence
    • Global stability

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