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    Pattern formation outside of equilibrium

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    A new method of analysis of the effect of weak colored noise in nonlinear dynamical systems

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    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 Hamilton-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. © 1987 Plenum Publishing Corporation.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
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