Effects of a degeneracy in a diffusive predator–prey model with Holling II functional response. (October 2018)

• Record Type: Journal Article
• Authors: Li, Shanbing; Wu, Jianhua; Dong, Yaying
• Is Part Of: Nonlinear analysis. Volume 43(2018)
• Page Start: 78
• Page End: 95
• Publication Date: 2018-10
• Subjects: Degeneracy -- Coexistence states -- Global bifurcation -- Asymptotic behavior; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.02.003
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this work, we study a spatially heterogeneous predator–prey model where the interaction is governed by a Holling II functional response. The existence of coexistence states of the two species by using the bifurcation theory is discussed. As a result, it is shown that the degeneracy for the prey and the predator has distinctly different effects on the coexistence states of the two species when the intrinsic growth rate of the prey is above a certain critical value. We also study the asymptotic behavior of positive stationary solutions as the intrinsic growth rate of the predator tends to a certain critical value.