Bifurcation Analysis of a Delayed Modified Holling-Tanner Predator-Prey Model with Refuge

Abstract

This paper deals with a delayed modified Holling-Tanner predator-prey model with refuge. The proposed model highlights the impact of delay and refuge on the dynamics of the system wherein analysis of the model in terms of local stability is performed. Both theoretical and experimental works point out that delay and refuge play an important role in the stability of the model and also it has been observed that due to delay, bifurcation occurred which results in considering delay as a bifurcation parameter. For some specific values of delay, Hopf bifurcation is investigated for the proposed model and direction of Hopf bifurcation with the stability of bifurcated periodic solutions by using normal form theory and central manifold reduction is also included in the domain of this study. At the end, few numerical simulations based on hypothetical set of parameters for the support of theoretical formulation are also carried out.