Sambath Muniyagounder - Department of Mathematics, Periyar University, Salem-۶۳۶۰۱۱, India
Ramajayam Sahadevan - Ramanujan Institute for Advanced Study in Mathematics, University of Madras, hennai-۶۰۰۰۰۵, India

In this paper, we have studied the diffusive predator-prey model with Monod-Haldane functional response. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated by analyzing the distribution of eigenvalues without diffusion. We also study the spatially homogeneous and non-homogeneous periodic solutions through all parameters of the system which are spatially homogeneous. In order to verify our theoretical results, some numerical simulations are also presented.

Stability, prey-predator, Monod-Haldane response, Hopf bifurcation