Invariant measure and numerical simulations for a stochastic predator–prey model — An example of verifying two-dimensional boundary measure integration

With the continuous development of the theory of stochastic biological population models, the study of the persistence of predator–prey models has become a very meaningful topic. This paper proves the sufficient conditions for the existence of a unique ergodic invariant measure for a three-dimensional stochastic predator–prey model with Markov switching, and subsequently proposes an approximate numerical method to verify the conditions of the two-dimensional boundary measure integration, thereby providing strong numerical support for the survival analysis of the model.