Markovian switching induced dynamics of a predator-prey system with prey refuge and habitat selection

In natural ecosystems, population dynamics are influenced by white and colored noise, which drive the population system to transition between multiple states. Therefore, it is essential to investigate predator-prey models that incorporate the concurrent impacts of white and colored noise. In this paper, we examined a three-dimensional stochastic predator-prey model involving dual prey species and a single predator by incorporating the refuge effect and habitat selection behavior under Markovian switching. By leveraging the theoretical framework of stochastic differential equations, its stochastic persistence was analyzed. Additionally, by constructing suitable Lyapunov functions, the conditions for an ergodic stationary distribution were deduced. Additionally, the extinction of populations and the asymptotic properties of solutions were explored. The findings revealed that habitat selection behavior has a significant and detrimental impact on the corresponding prey, while the refuge effect positively influences the prey and the predator. Ultimately, numerical simulations were performed to validate the theoretical outcomes. The results of these simulations strongly confirm the accuracy of the theoretical deductions.