Coupling-induced dynamics in a stochastic two-predator two-prey system with Markov switching

We investigate a four-dimensional coupled predator-prey model that integrates white noise to model continuous environmental fluctuations and Markov switching to characterize discrete regime shifts. Compared with classical two-dimensional models, this formulation allows a more realistic description of complex multispecies interactions. In the deterministic case, the stability and bifurcation conditions for positive equilibrium are derived theoretically. The results show that increasing the coupling strength can induce Andronov-Hopf bifurcations and spiral dynamics, leading the system to evolve from a stable coexistence state to multimodal oscillations. In stochastic settings, the stochastic P-bifurcation phenomenon caused by noise and switching is identified through changes in the stationary probability density functions and the most probable trajectories. Based on the most probable trajectory theory, a quantitative indicator is further introduced to determine the bifurcation conditions in the switched system and to evaluate species coexistence in a switching environment. Results indicate that weak noise and switching rate can increase the coupling-induced bifurcation threshold and weaken multimodal oscillations. The combined influence of these factors provides a guiding basis for the coexistence of multiple species in switching environments.