Existence of spatial patterns in a predator–prey model with self- and cross-diffusion

In this work, we investigate the spatiotemporal dynamics of reaction–diffusion equations subject to cross-diffusion in the frame of a two-dimensional ratio-dependent predator–prey model. The conditions for diffusion-driven instability are obtained and the Turing space in the parameters space is achi...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 226; pp. 320 - 335
Main Author Guin, Lakshmi Narayan
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.2014
Subjects
Asymptotic properties
Diffusion
Dynamic tests
Instability
Mathematical analysis
Mathematical models
Predator–prey model
Reaction–diffusion equations
Spatial pattern
Stability
Steady state
Turing instability
Reaction–diffusion equations
Spatial pattern
Stability
Turing instability
Predator–prey model
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Summary:In this work, we investigate the spatiotemporal dynamics of reaction–diffusion equations subject to cross-diffusion in the frame of a two-dimensional ratio-dependent predator–prey model. The conditions for diffusion-driven instability are obtained and the Turing space in the parameters space is achieved. Moreover, the criteria for local and global asymptotic stability of the unique positive homogeneous steady state without diffusion are discussed. Numerical simulations are carried out in order to validate the feasibility of the obtained analytical findings. Different types of spatial patterns through diffusion-driven instability of the proposed model are portrayed and analysed. Lastly, the paper finishes with an external discussion of biological relevance of the analysis regarding cross-diffusion and pattern issues.
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2013.10.005