Population explosion suppressed by noise: Stationary distributions and how to simulate them

Details Population explosion suppressed by noise: Stationary distributions and how to simulate them Population explosion suppressed by noise: Stationary distributions and how to simulate them

2004-12-17

arxiv.org/abs/cond-mat/0412476v1

Physics

Condensed Matter

Statistical Mechanics

New Journal of Physics, submitted

Scientific paper

We show that two dynamical systems exhibiting very different deterministic behaviours possess very similar stationary distributions when stabilized by a multiplicative Gaussian white noise. We also discuss practical aspects of numerically simulating these systems. We show that there exists a noise level that is optimal in the sense that the interval during which discrete-time versions of the systems remain physical is maximized. Analytical results are illustrated by numerical examples.

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