Spatial patterns of a predator-prey model with cross diffusion

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 difG.-Q. Sun ( ) · Z. Jin · L. Li Department of Mathematics, North University of China, Taiyuan, Shan’xi 030051, People’s Republic of China e-mail: [email protected] Z. Jin e-mail: [email protected] L. Li e-mail: [email protected] M. Haque Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD UK e-mail: [email protected] B.-L. Li Ecological Complexity and Modeling Laboratory, Department of Botany and Plant Sciences, University of California, Riverside, CA 92521-0124, USA e-mail: [email protected] fusion can create stationary patterns, which enrich the finding of pattern formation in an ecosystem.