Stationary Response of Switching Ecosystems Under Correlated Noise Excitations

A stochastic predator-prey system with Markov switching and colored noise is studied, where Markov switching is used to represent parameter changes caused by environmental mutations. The joint impact of switching and colored noise on the stationary response is explored by the stochastic averaging method, the stochastic Runge-Kutta algorithm, and the most probable trajectory theory. Findings show that a wider bandwidth tends to make the stationary response more concentrated and drives the most probable response closer to the deterministic one, whereas a narrower bandwidth is associated with stronger population oscillations. A larger stationary probability tends to drive the system response toward that of the corresponding substate, while a faster transition rate generally stabilizes the most probable response. In addition, both the bandwidth parameter and switching may induce stochastic P-bifurcation, accompanied by changes in the concentration and shape of the stationary distribution. The results also indicate that the overall stationary response is influenced not only by stationary probabilities but also by the intrinsic stability of the substates.