Spatial patterns of a predator-prey model with cross diffusion

Gui-Quan Sun, Zhen Jin, Li Li, Mainul Haque, Bai-lian Li

Research output: Contribution to journalArticlepeer-review


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
JournalNonlinear Dynamics
Issue number4
Early online date13 Mar 2012
Publication statusPublished - 1 Sept 2012


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