Abstract
In this paper, a food chain system with gestation delay for both pest and the natural enemy is proposed. Here the boundedness of the system is studied. Stability analysis for all possible equilibrium points is carried out. The thresholds for Hopf bifurcation at interior and the natural enemy free equilibrium states are studied and analyzed. It is observed that the natural enemy free steady state is stable if the gestation delay for the pest is sufficiently low otherwise system observed oscillating behavior. Similar observations established for the interior equilibrium. The sensitivity analysis is performed to find the respective sensitive indices of the variables of the proposed system. Further, simulations have been carried out to support our analytic results.
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