Survivability analysis for a three-dimensional predator–prey model with Markov switching

Predator–prey model is a classic biological model used to study the relationship between species survival. In this study, we investigate a stochastic single predator–dual prey model with Beddington–DeAngelis functional response and Markov switching. The main contribution of this paper is that we give the integrity analysis of all possible living states, and also give the corresponding numerical simulations by python software. Survival conditions in this paper are obtained based on integrations about the stationary distributions of some auxiliary equations. One point of interest is the verification of survival conditions in numerical simulations. First, the integration with respect to stationary measure is calculated for each state, and then the averaged value is obtained by using the stationary distribution of the Markov chain.