TY - JOUR
T1 - A novel stochastic bifurcation and its discrimination
AU - Jin, Chen
AU - Sun, Zhongkui
AU - Xu, Wei
N1 - Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/7
Y1 - 2022/7
N2 - 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.
AB - 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.
KW - Bifurcation discrimination
KW - Stochastic bifurcation
KW - Stochastic dynamic system
KW - Stochastic extremum bifurcation
UR - http://www.scopus.com/inward/record.url?scp=85125736330&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2022.106364
DO - 10.1016/j.cnsns.2022.106364
M3 - 文章
AN - SCOPUS:85125736330
SN - 1007-5704
VL - 110
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
M1 - 106364
ER -