The spatial patterns through diffusion-driven instability in a predator-prey model

Lakshmi Narayan Guin, Mainul Haque, Prashanta Kumar Mandal

Research output: Journal PublicationArticlepeer-review

32 Citations (Scopus)

Abstract

Studies on stability mechanism and bifurcation analysis of a system of interacting populations by the combined effect of self and cross-diffusion become an important issue in ecology. In the current investigation, we derive the conditions for existence and stability properties of a predator-prey model under the influence of self and cross-diffusion. Numerical simulations have been carried out in order to show the significant role of self and cross-diffusion coefficients and other important parameters of the system. Various contour pictures of spatial patterns through Turing instability are portrayed and analysed in order to substantiate the applicability of the present model. Finally, the paper ends with an extended discussion of biological implications of our findings.

Original languageEnglish
Pages (from-to)1825-1841
Number of pages17
JournalApplied Mathematical Modelling
Volume36
Issue number5
DOIs
Publication statusPublished - May 2012
Externally publishedYes

Keywords

  • Diffusion-driven instability
  • Hopf-bifurcation
  • Predator-prey model
  • Reaction-diffusion system
  • Self and cross-diffusion
  • Simulation

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

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