Stability of a three-species stochastic delay predator-prey system with Lévy noise (Q2149142)

This paper is concerned with a predator-prey model with herd behavior and prey-taxis. Authors first analyze the stability and bifurcation of the positive equilibrium of the model subject to the homogeneous Neumann boundary condition. And then he obtain a branch of stable nonconstant solutions bifurcating from the positive equilibrium by using an abstract bifurcation theory and taking prey-tactic sensitivity coefficient as the bifurcation parameter. The results show that prey-taxis can yield the occurrence of spatial patterns.