Hopf bifurcation analysis in a Monod-Haldane predator-prey model with delays and diffusion

In this paper we consider a three-species model with Monod-Haldane functional response and diffusion. By analyzing the associated characteristic equation, we demonstrate the local stability of the positive equilibrium and the existence of Hopf bifurcation. We can derive explicit formulas to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solution using the normal form method and center manifold theorem. Numerical simulations illustrate the results.