Du, Yihong

Peng, Rui

Wang, Mingxin

2009

In this paper, we consider the diffusive Leslie predator-prey model with large intrinsic predator growth rate, and investigate the change of behavior of the model when a simple protection zone Ω₀ for the prey is introduced. As in earlier work [Y. Du, J. Shi. A diffusive predator-prey model with a protection zone. J. Differential Equations 229 [2006] 63-91: Y. Du. X. Liang. A diffusive competition model with a protection zone. J. Differential Equations 244 (2008) 61-86] we show the existence of a critical patch size of the protection zone, determined by the first Dirichlet eigenvalue of the Laplacian over Ω₀ and the intrinsic growth rate of the prey, so that there is fundamental change of the dynamical behavior of the model only when Ω₀ is above the critical patch size. However, our research here reveals significant difference of the model's behavior from the predator-prey model studies in [Y. Du, J. Shi, A diffusive predator-prey model with a protection some, J. Differential Equations 229 (2006) 63-91] with the same kind of protection zone. We show that the asymptotic profile of the population distribution of the Leslie model is governed by a standard boundary blow-up problem, and classical or degenerate logistic equations.

Journal of Differential Equations, 246(10), p. 3932-3956

1090-2732

0022-0396

https://hdl.handle.net/1959.11/3627

Academic Press

Effect of a protection zone in the diffusive Leslie predator-prey model

Journal Article

Publication