ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 60, 65 Volker Wihstutz, University of North Carolina at Charlotte, NC Stability Maps for Systems with Noise Induced Stability A system like an inverted pendulum standing on a membrane can be stabilized by randomly vibrating the supporting membrane, provided suitable noise is used. (White noise, d(Wiener), is not suitable, but d(Ornstein-Uhlenbeck) is.) The originally unstable equilibrium becomes stable, if the top Lyapunov exponent L associated with the noise perturbed system becomes negative. The generator of such a system is non-elliptic. Stochastic numerical schemes are discusssed to compute L as function of damping b and noise intensity 1/epsilon for such a degenerate system; in particular, the border line L(b, epsilon)=0 is considered.