Spatial patterns of a predator-prey model with cross diffusion

Gui Quan Sun, Zhen Jin, Li Li, Mainul Haque, Bai Lian Li

Research output: Journal PublicationArticlepeer-review

72 Citations (Scopus)


In this paper, spatial patterns of a Holling- Tanner predator-prey model subject to cross diffusion, which means the prey species exercise a self-defense mechanism to protect themselves from the attack of the predator are investigated. By using the bifurcation theory, the conditions of Hopf and Turing bifurcation critical line in a spatial domain are obtained. A series of numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, such as spotted, stripe-like, or labyrinth patterns. Our results confirm that cross diffusion can create stationary patterns, which enrich the finding of pattern formation in an ecosystem.

Original languageEnglish
Pages (from-to)1631-1638
Number of pages8
JournalNonlinear Dynamics
Issue number4
Publication statusPublished - Sept 2012
Externally publishedYes


  • Cross diffusion
  • Pattern formation
  • Predator-prey

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering


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