Analysis Of Spatial Structure In A Predator-Prey Model With Delay .2. Nonlinear-Theory

    Authors

    S. R. Choudhury

    Comments

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    Abbreviated Journal Title

    SIAM J. Appl. Math.

    Keywords

    PREDATOR-PREY MODELS WITH DIFFUSION AND DELAY; NONLINEAR SPATIAL; STRUCTURE AND PATTERN FORMATION; WEAK GENERIC KERNEL; GINZBURG-LANDAU EQUATION; BIOLOGICAL PATTERN; Mathematics, Applied

    Abstract

    A nonlinear stability analysis using a multiple-scales perturbation procedure is performed for a predator-prey model including spatial diffusion and Volterra-type distributed delays in the interspecies interaction terms. For delays modeled by the ''weak'' generic kernel, the slow evolution of the amplitude of the spatially nonuniform states predicted by the linear analysis is shown to be governed by a complicated Ginzburg-Landau/Newell-Whitehead equation. Both the spatially-dependent and space-independent versions of this equation are analyzed to obtain the regimes of the physical parameter space where the linear nonuniform solutions either asymptote to a fixed amplitude wave pattern with an amplitude dependent frequency modulation, evolve to other permanent spatially-dependent wave solutions or patterns via nonlinear modulational instability, or decay to zero.

    Journal Title

    Siam Journal on Applied Mathematics

    Volume

    54

    Issue/Number

    5

    Publication Date

    1-1-1994

    Document Type

    Article

    Language

    English

    First Page

    1451

    Last Page

    1467

    WOS Identifier

    WOS:A1994PJ21500014

    ISSN

    0036-1399

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