Bifurcation Analysis in the Stochastic Lumped Parameter System

This paper is concerned with a bifurcation analysis of a stochastic lumped parameter 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 diagrams. So, we study the bifurcation in the stochastic lumped parameter system by the D-bifurcation approach.