Chinese Journal of Theoretical and Applied Mechani ›› 1997, Vol. 29 ›› Issue (2): 158-166.DOI: 10.6052/0459-1879-1997-2-1995-211

• Research paper • Previous Articles     Next Articles

ON THE HOPF BIFURCATION SYSTEM IN THE PRESENCE OF PARAMETRIC REAL NOISES

,   

  1. 西南交通大学工程力学系
  • Received:1900-01-01 Revised:1900-01-01 Online:1997-03-25 Published:1997-03-25

Abstract: With the aid of the stochastic averaging method,the theory of singular points of diffusion processes and the method of invariant measure, a Hopf bifurcation system in the presence of parametric real noises is studied. It is found that in this nonlinear stochastic system, due tothe presence of the parametric real noises, a change of the type of bifurcation takes place and two bifurcation points appear, which differ from the original Hopf bifurcation one.

Key words: real noise, parametric excitation, stochastic averaging method, diffusion process, singular boundary, invariant measure, stochastic bifurcation