Dynamics in a diffusive predator–prey system with a constant prey refuge and delay. (October 2016)

• Record Type: Journal Article
• Authors: Yang, Ruizhi; Zhang, Chunrui
• Is Part Of: Nonlinear analysis. Volume 31(2016)
• Page Start: 1
• Page End: 22
• Publication Date: 2016-10
• Subjects: Prey–predator -- Delay -- Turing instability -- Hopf bifurcation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.01.005
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, a diffusive predator–prey system with a constant prey refuge and time delay subject to Neumann boundary condition is considered. Local stability and Turing instability of the positive equilibrium are studied. The effect of time delay on the model is also obtained, including locally asymptotical stability and existence of Hopf bifurcation at the positive equilibrium. And the properties of Hopf bifurcation are determined by center manifold theorem and normal form theorem of partial functional differential equations. Some numerical simulations are carried out. Highlights: A diffusive predator–prey system with a constant prey refuge and time delay is considered. The stability and Turing instability of the positive equilibrium are obtained. The existence of Hopf bifurcation at the positive equilibrium is obtained. The direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are determined.