Hopf Bifurcation in a Delayed Predator-prey System with Stage Structure and Crowley-Martin Functional Response

In this paper,we analyze a delayed and stage-structured predator-prey system with Crowley-Martin functional response.By analyzing the distribution of the roots of the associated characteristic equation,sufficient conditions for the local asymptotic stability of the positive equilibrium and the existence of the periodic solutions via Hopf bifurcation with respect to the time delay are obtained.Direction of the Hopf bifurcation and the stability of the periodic solutions that bifurcate from Hopf bifurcation are established by using the normal form theory and center manifold argument.Finally,numerical simulation results are given to support the analytical findings.