Stability and turing instability in a diffusive predator–prey system with Beddington–DeAngelis functional response

A diffusive two-species predator–prey system with the Beddington–DeAngelis functional response and subject to homogeneous Neumann boundary conditions is considered. In the region of parameters where the positive constant steady state is globally asymptotically stable when there exists no diffusion,...

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Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 20; pp. 1 - 13
Main Authors Yan, Xiang-Ping, Zhang, Cun-Hua
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.12.2014
Subjects
Asymptotic properties
Beddington–DeAngelis functional response
Boundary conditions
Constants
Diffusion
Global asymptotic stability
Impact analysis
Instability
Reaction–diffusion system
Stability
Steady state
Turing instability
Global asymptotic stability
Reaction–diffusion system
Turing instability
Beddington–DeAngelis functional response
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ISSN1468-1218
1878-5719
DOI10.1016/j.nonrwa.2014.04.001

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Summary:A diffusive two-species predator–prey system with the Beddington–DeAngelis functional response and subject to homogeneous Neumann boundary conditions is considered. In the region of parameters where the positive constant steady state is globally asymptotically stable when there exists no diffusion, the impact of the diffusion on the stability is analyzed in detail. The global asymptotic stability of the positive constant steady state is also considered by means of the upper and lower solutions method and the monotone iteration principle.
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ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2014.04.001