Spatiotemporal dynamics of a diffusive Leslie-Gower predator-prey model with ratio-dependent functional response

Hong Bo Shi, Shigui Ruan, Ying Su, Jia Fang Zhang

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

This paper is devoted to the study of spatiotemporal dynamics of a diffusive Leslie-Gower predator-prey system with ratio-dependent Holling type III functional response under homogeneous Neumann boundary conditions. It is shown that the model exhibits spatial patterns via Turing (diffusion-driven) instability and temporal patterns via Hopf bifurcation. Moreover, the existence of spatiotemporal patterns is established via Turing-Hopf bifurcation at the degenerate points where the Turing instability curve and the Hopf bifurcation curve intersect. Various numerical simulations are also presented to illustrate the theoretical results.

Original languageEnglish (US)
Article number1530014
JournalInternational Journal of Bifurcation and Chaos
Volume25
Issue number5
DOIs
StatePublished - May 26 2015

Keywords

  • Diffusive predator-prey model
  • Hopf bifurcation
  • Turing instability
  • Turing-Hopf bifurcation
  • functional response
  • stability

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

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