Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
1997-07-31
Nonlinear Sciences
Adaptation and Self-Organizing Systems
Plain Tex, 10 pages, 2 postscript figures included
Scientific paper
We consider a slow passage through a point of loss of stability. If the passage is sufficiently slow, the dynamics are controlled by additive random disturbances, even if they are extremely small. We derive expressions for the `exit value' distribution when the parameter is explicitly a function of time and the dynamics are controlled by additive Gaussian noise. We derive a new expression for the small correction introduced if the noise is coloured (exponentially correlated). There is good agreement with results obtained from simulation of sample paths of the appropriate stochastic differential equations. Multiplicative noise does not produce noise-controlled dynamics in this fashion.
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