Communications on Pure and Applied Analysis
A delayed diffusive predator-prey system with Holling type-II predator functional response subject to Neumann boundary conditions is considered here. The stability/instability of nonnegative equilibria and associated Hopf bifurcation are investigated by analyzing the characteristic equations. By the theory of normal form and center manifold, an explicit formula for determining the stability and direction of periodic solution bifurcating from Hopf bifurcation is derived.
Chen, S., Shi, J., & Wei, J. (2013). The effect of delay on a diffusive predator-prey system with Holling type-II predator functional response. Communications on pure and applied analysis, 12(1), 481-501.