Title

Analysis Of Spatial Structure In A Predator-Prey Model With Delay Ii: Nonlinear Theory

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.

Publication Date

1-1-1994

Publication Title

SIAM Journal on Applied Mathematics

Volume

54

Issue

5

Number of Pages

1451-1467

Document Type

Article

Identifier

scopus

Personal Identifier

scopus

DOI Link

https://doi.org/10.1137/S0036139993247252

Socpus ID

0028518446 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0028518446

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