Bifurcation branch and stability of stationary solutions of a predator–prey model

ABSTRACT

This paper is concerned about a diffusive degenerate predator–prey model with Beddington–DeAngelis functional response subject to homogeneous Neumann boundary condition. First, the global bifurcation branches of positive stationary solutions are studied, which are quite different from those with different degeneracy or functional response. Second, the multiplicity and stability of positive stationary solutions are obtained as the parameter k or m in the Beddington–DeAngelis functional response is large enough, from which the effects of the functional response on the coexistence region are revealed. In particular, the global stability of the positive stationary solution is derived as it exists uniquely.

Keywords:

• Predator–prey model
• spatial heterogeneity
• Beddington–DeAngelis functional response
• bifurcation
• global stability

2010 Mathematics Subject Classifications:

• 35J60
• 92D25
• 35B32

Acknowledgments

The author would like to thank the anonymous reviewers for the valuable and useful suggestions on the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).