A novel stochastic bifurcation and its discrimination

This paper is concerned with a novel stochastic bifurcation and its discrimination of stochastic dynamical system. A new kind of stochastic response—called extremely possible response and a novel stochastic bifurcation—called stochastic extremum bifurcation is defined for the first time. An entirely new method for discriminating stochastic bifurcation is proposed based on the new definition mentioned above. In addition, the classical Van der Pol oscillator is used as the illustrative example to demonstrate the validity of the proposed method. Worthy of note is that the new stochastic extremum bifurcation defined in this paper is mathematically equivalent to the stochastic P-bifurcation defined by Arnold and the new proposed method for discriminating stochastic bifurcation is more convenient than the “traditional” method.