Complex dynamics of delay induced two-prey one-predator model with Beddington-DeAngelis response function

Abstract

In view of the logical consistence, the model of a two-prey one-predator system with Beddington DeAngelis functional response and consideration of time delay is formulated and studied systematically. The Beddington–DeAngelis functional response is similar to the Holling type II functional response but contains an extra term describing mutual interference by predators. As the effect of time delay which is due to the gestation or digestion of the prey and predator respectively, hence the ordinary differential equation of the model is replaced by delay differential equation and therefore the solution of the system is studied without and with delay. Dynamical behaviours such as boundedness, local stability and persistence of the model are studied. Also criteria are derived for the existence of a globally stable coexistence equilibrium. At the end numerical simulation is performed to check the validation of the analytical findings.