Complex dynamical behaviour of predator-prey model with harvesting and multiple delays

In this work, we investigate a predator-prey model with Crowley-Martin functional response and constant harvesting. The model is extended by incorporating two constant time delays, where the first delay(tau(1)) is for density dependent feedback mechanism in the logistic growth of the prey and the second one is for gestation delay(tau(2)) of the predator population. The dynamical behaviours such as positivity, boundedness, extinction criteria and existence, stability and bifurcations of the equilibria of the non-delay model are qualitatively discussed. The existence of periodic solutions via Hopf-bifurcation with respect to absence of delay, single delay and both delays are established. Finally, numerical simulations have been carried out to confirm our numerical results.