Bifurcation analysis of coexistent state in a delayed two-species predator-prey model. Issue 7 (18th May 2020)

• Record Type: Journal Article
• Authors: Ma, Li; Xie, Xianhua
• Is Part Of: Applicable analysis. Volume 99:Issue 7(2020)
• Page Start: 1195
• Page End: 1217
• Publication Date: 2020-05-18
• Subjects: Simple eigenvalue -- time delay -- comparison principle -- bifurcation theory -- Lyapunov-Schmidt reduction -- Hopf bifurcation; 35B40 -- 35K57 -- 92D25; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1529302
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we consider a delayed two-species predator-prey model with general functional response under the homogeneous Neumann boundary condition. We discuss the stability of the trivial and semi-trivial solutions and obtain the spatially nonhomogeneous bifurcation solutions stemming from the semi-trivial trivial solutions ( θ a, 0 ) and ( 0, θ b ) . Besides, the stability and some results of Hopf bifurcation at the spatially nonhomogeneous bifurcation steady-state solutions are investigated by analyzing the distribution of the eigenvalues. The method we applied here is mainly based on spectral analysis, comparison principle, Lyapunov-Schmidt reduction, and bifurcation theory.