Abstract
In the present paper, prey-predator relationship is discussed using Holling type IV functional response. Modified Holling-tanner prey-predator model has been considered and time delay has been incorporated in the system which is a parameter of bifurcation. The concept of migration in prey and predator population is induced in the system along with prey refuge and local stability analysis has been carried out. The direction of Hopf bifurcation along with the stability of periodic solutions is investigated using central manifold reduction and normal form theory. It is examined that delay plays a dominant role in stabilizing the system, as a consequence critical values of delay occurs below and above which, the dynamics of the system changes. Numerical simulation highlighting the role of migration and to validate theoretical results is presented at the end.
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