A delayed-diffusive predator-prey model with a ratio-dependent functional response

Abstract In this paper, a delayed-diffusive predator-prey model with a ratio-dependent functional response subject to Neumann boundary condition is studied. More precisely, Turing instability of positive equilibrium, instability and Hopf bifurcation induced by time delay are discussed. In addition, by the theory of normal form and center manifold, conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution are derived. Numerical simulations are conducted to illustrate the theoretical analysis.

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