论文信息 - Bifurcations of One-Dimensional Stochastic Differential Equations

Bifurcations of One-Dimensional Stochastic Differential Equations

We consider families of random dynamical systems induced by parametrized one-dimensional stochastic differential equations. We give necessary and sufficient conditions on the invariant measures of the associated Markov semigroups which ensure a stochastic bifurcation. This leads to sufficient conditions on drift and diffusion coefficients for a stochastic pitchfork and transcritical bifurcation of the family of random dynamical systems.

[1] Werner Horsthemke,et al. Noise-induced transitions , 1984 .

[2] L. Arnold,et al. Stochastic bifurcation: instructive examples in dimension one , 1992 .

[3] S. Krenk,et al. IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics : proceedings of the IUTAM Symposium held in Trondheim, Norway, 3-7 July 1995 , 1996 .

[4] F. Ledrappier. Positivity of the exponent for stationary sequences of matrices , 1986 .

[5] Ioannis Karatzas,et al. Brownian Motion and Stochastic Calculus , 1987 .

[6] Y. le Jan,et al. Equilibre statistique pour les produits de difféomorphismes aléatoires indépendants , 1986 .

[7] L. Arnold,et al. Fixed Points and Attractors for Random Dynamical Systems , 1996 .

[8] H. Crauel. Non-Markovian invariant measures are hyperbolic , 1993 .

[9] Hans Crauel,et al. Additive Noise Destroys a Pitchfork Bifurcation , 1998 .

[10] Peter H. Baxendale,et al. Asymptotic behaviour of stochastic flows of diffeomorphisms , 1986 .

[11] Hans Crauel,et al. Markov measures for random dynamical systems , 1991 .

[12] M. Scheutzow,et al. Perfect cocycles through stochastic differential equations , 1995 .