Mathematical analysis of prey predator models with Holling type I functional responses and time delay

Abstract

We examine two prey and one predator models with Holling type I functional behaviours in this paper. To demonstrate the system’s permanence and boundedness, we used a discrete-time delay. Through the use of traditional mathematical techniques, the effects of random variations in the environment and time delay on the model’s stability are analytically examined. The stability and Hopf-Bifurcation for the competition model are also described and shown. A few numerical computations are provided to demonstrate the efficacy of the theoretical findings.