On the Bifurcation Analysis of the Stochastic Predator-prey System based on the D-bifurcation

This research is concerned with a bifurcation analysis of a stochastic predator-prey system. The P-bifurcation (Phenomenological bifurcation) and the D-bifurcation (Dynamical bifurcation) are major analytical methods for the stochastic bifurcation. The P-bifurcation studies a stationary measure corresponding to the one-point motion, while the D-bifurcation approach is based on the stability of invariant measures. Since the P-bifurcation is based on the one point-motion, there is a possibility to miss certain branches in bifurcation. So, we study the bifurcation of the stochastic predator-prey system with help of the D-bifurcation, and analyze the influence of the random noise on the bifurcation phenomena in the proposed stochastic model.