Bifurcation analysis of coexistent state in a delayed two-species predator-prey model.

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. [ABSTRACT FROM AUTHOR]