Abstract
In this paper, by using the Beurling-Nevanlinna type inequality we obtain new results on the existence of solutions of the Dirichlet problem with respect to the Schrödinger-prey operator. Meanwhile, the local stability of the Schrödingerean equilibrium and endemic equilibrium of the model are also discussed. We specially analyze the existence and stability of the Schrödingerean Hopf bifurcation by using the center manifold theorem and bifurcation theory. As applications, theoretic analysis and numerical simulation show that the Schrödinger-prey system with latent period has a very rich dynamic characteristics.