Title

Turing Bifurcation In Nonlinear Competition Models With Delay

Keywords

Delay; Reaction-diffusion and predator-prey models; Turing bifurcations or instability

Abstract

Turing instability in reaction-diffusion and predator-prey models including diffusion and Volterra-type distributed delays in the interspecies interaction terms is considered. For general functional forms of the reaction terms/prey birth rate-predator death rate, and delays modeled by the "weak" generic kernel a exp(-aU) and the "strong" generic kernel a2U exp(-aU), the necessary and sufficient conditions for Turing instability are derived and are found to be significantly different from the classical conditions with no delay. The structure of the resulting Turing space, where steady states may be diffusionally driven unstable initiating spatial patterns, is delineated for four 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.

Publication Date

1-1-1996

Publication Title

Quarterly of Applied Mathematics

Volume

54

Issue

1

Number of Pages

33-61

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/qam/1373837

Socpus ID

1842794537 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/1842794537

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