Stochastic bifurcation and Break-out of dynamic balance of predator-prey system with Markov switching

A B S T R A C T This paper investigates Markov-switching-induced stochastic P-bifurcation and the dy-namical balance in a predator-prey system. Based on the limit averaging, a probability -weighted system is established to approximate the original stochastic switching ecosystem, then the stationary distribution and first-passage problems are theoretically addressed. Stochastic bifurcations are discussed through a qualitative change of the stationary prob-ability density, which indicates that the transition rate matrix of Markov switching can be treated as a bifurcation parameter. They also imply that the stationary distribution is more sensitive to the transition rate lambda 12. Besides, by the first-passage theory, the dynamic balance is explored to elucidate the mechanisms underlying species coexistence. Aston-ishingly, the Markov switching may maintain or even improve the dynamic stability of species coexistence. Biologically, apart from human destruction, the species are even more robust and capable of adapting to general environmental disturbances. The utility and the accuracy of the theoretical analysis are demonstrated by direct numerical simulations.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This paper investigates the dynamics of a predator-prey system under Markov-switching-induced stochastic P-bifurcation. The research establishes a probability-weighted system to approximate the original stochastic switching ecosystem and addresses the stationary distribution and first-passage problems theoretically. Stochastic bifurcations are discussed by examining the qualitative change of the stationary probability density, which indicates that the transition rate matrix of Markov switching acts as a bifurcation parameter. Furthermore, the study explores the dynamic balance using the first-passage theory and reveals that the Markov switching can maintain or improve the stability of species coexistence.