On the low-dimensional modelling of Stratonovich stochastic differential equations

Details On the low-dimensional modelling of Stratonovich stochastic differential equations On the low-dimensional modelling of Stratonovich stochastic differential equations

1997-04-30

arxiv.org/abs/chao-dyn/9705002v1

Nonlinear Sciences

Chaotic Dynamics

LaTeX2e, 272K (including ps figs), 23pp Keywords: stochastic differential equation, centre manifold, low-dimensional modelling

Scientific paper

We develop further ideas on how to construct low-dimensional models of stochastic dynamical systems. The aim is to derive a consistent and accurate model from the originally high-dimensional system. This is done with the support of centre manifold theory and techniques. Aspects of several previous approaches are combined and extended: adiabatic elimination has previously been used, but centre manifold techniques simplify the noise by removing memory effects, and with less algebraic effort than normal forms; analysis of associated Fokker-Plank equations replace nonlinearly generated noise processes by their long-term equivalent white noise. The ideas are developed by examining a simple dynamical system which serves as a prototype of more interesting physical situations.

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