Bifurcation branch of stationary solutions in a general predator–prey system with prey-taxis. (1st July 2019)

• Record Type: Journal Article
• Authors: Kong, Lei; Lu, Fengjiao
• Is Part Of: Computers & mathematics with applications. Volume 78:issue 1(2019)
• Page Start: 191
• Page End: 203
• Publication Date: 2019-07-01
• Subjects: Predator–prey model -- Prey-taxis -- Reaction–diffusive system -- Global bifurcation -- A priori estimates; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.02.023
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, a general reaction–diffusive predator–prey system with prey-taxis subject to the homogeneous Neumann boundary condition is considered. Firstly, we investigate the local stability of the unique positive equilibrium by analyzing the characteristic equation and study a priori estimates of positive solutions by the iterative technique. And then, choosing the prey-tactic sensitivity coefficient as bifurcation parameter, we proved that a branch of nonconstant solutions can bifurcate from the unique positive equilibrium when the prey-tactic sensitivity is repulsive. Moreover, we find the stable bifurcating solutions near the bifurcation point by the spectrum theory under some suitable conditions. Our results show that prey-taxis can destabilize the uniform equilibrium and yields the occurrence of spatial patterns.