New method of analysis of the effect of weak colored noise in nonlinear dynamical systems
A systematic method for obtaining the asymptotic behavior of a dynamical system forced by colored noise in the limit of small intensity is developed. It is based on the search of WKB solutions to the Fokker-Planck equation for the joint probability density of the system and noise, in which the perturbation expansion is continued to the first correction beyond the Hamiltonian-Jacobi limit. The method can be applied to noise with correlation time of order unity. It is illustrated on the normal form of a pitchfork bifurcation, where it is pointed out that additive noise can induce a shift of the most probable value. This prediction is confirmed by numerical simulation of the stochastic differential equations.
- Research Organization:
- Faculte des Sciences, Universite Libre de Bruxelles, 1050 Bruxelles, Belgium
- OSTI ID:
- 6686864
- Journal Information:
- J. Stat. Phys.; (United States), Vol. 46:1
- Country of Publication:
- United States
- Language:
- English
Similar Records
Can colored noise improve stochastic resonance
Probabilistic density function method for nonlinear dynamical systems driven by colored noise