Strategy and stationary pattern in a three-species predator–prey model

doi:10.1016/j.jde.2004.01.004

Journal of Differential Equations

Volume 200, Issue 2, 10 June 2004, Pages 245-273

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Abstract

In this paper, we study a strongly coupled system of partial differential equations which models the dynamics of a two-predator-one-prey ecosystem in which the prey exercises a defense switching mechanism and the predators collaboratively take advantage of the prey's strategy. We demonstrate the emergence of stationary patterns for this system, and show that it is due to the cross diffusion that arises naturally in the model. As far as the authors are aware, this is the first example of stationary patterns in a predator–prey system arising solely from the effect of cross diffusion.

MSC

35J55

92D25

Keywords

Predator–prey model

Cross diffusion

Strongly coupled elliptic system

Stationary pattern

Cited by (0)

¹: The work of this author was supported by the NUS ARF Grant R-146-000-034-112.

²: Part of the paper was done during the visit to the National University of Singapore. He expresses his gratitude to the support of the NUS ARF Grant R-146-000-034-112, the PRC NSF Grant NSFC-19831060 and the “333” Project of JiangSu Province, China.