Turing Instability In Competition Models With Delay .1. Linear-Theory

    Authors

    S. R. Choudhury

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    SIAM J. Appl. Math.

    Keywords

    TURING BIFURCATIONS OR INSTABILITY; DELAY; PREDATOR-PREY AND; REACTION-DIFFUSION MODELS; BIOLOGICAL PATTERN-FORMATION; PREDATOR PREY MODEL; STABLE OSCILLATIONS; COAT MARKINGS; TIME-LAG; MECHANISMS; SPACE; Mathematics, Applied

    Abstract

    Turing instability in two-component predator-prey and reaction-diffusion models including diffusion and Volterra-type distributed delays in the interspecies interaction terms is considered. For general functional forms of the prey birthrate-predator deathrate/reaction terms and delays modeled by the ''weak'' generic kernel a exp(-aU) or the ''strong'' generic kernel aU exp(-aU), the structure of the diffusively-unstable space is shown to be completely altered by the inclusion of delays. The necessary and sufficient conditions for Turing instability are derived using the ''weak'' generic kernel and are found to be significantly different from the classical conditions with no delay. The structure of the Turing space, where steady states may be diffusionally driven unstable initiating spatial pattern, is delineated for several specific models, and compared to the corresponding regimes in the absence of delay. An alternative bifurcation-theoretic derivation of the boundary of the Turing-unstable domain is also presented. Finally, the instability with delays is briefly considered for two spatial dimensions and a finite domain size.

    Journal Title

    Siam Journal on Applied Mathematics

    Volume

    54

    Issue/Number

    5

    Publication Date

    1-1-1994

    Document Type

    Article

    Language

    English

    First Page

    1425

    Last Page

    1450

    WOS Identifier

    WOS:A1994PJ21500013

    ISSN

    0036-1399

    Share

    COinS