Threshold of a stochastic two-species predator-prey model

Abstract

We consider a predator-prey model with the Beddington-DeAngelis functional response in a deterministic framework. Further, we include harvesting, and finally, we introduce stochasticity. First, we analyze key findings for the deterministic framework, including the system’s equilibria and their stability. For the stochastic version, we use appropriate Lyapunov functions and integrate the knowledge of stochastic differential equations to establish the conditions under which both the prey and predator will become extinct. Subsequently, we determine the condition for the predator extinction while the prey continues to exist. Moreover, we explore the existence of unique positive global solutions for this model. Finally, we present some numerical simulations for time responses for the population.