Europhys. Lett.
Volume 66, Number 2, April 2004
Page(s) 185 - 191
Section General
Published online 01 April 2004
Europhys. Lett., 66 (2) , pp. 185-191 (2004)
DOI: 10.1209/epl/i2003-10201-5

Noisy limit point bifurcation with a slowly varying control parameter

C. Nicolis1 and G. Nicolis2

1  Institut Royal Météorologique de Belgique 3, Avenue Circulaire, 1180 Brussels, Belgium
2  Center for nonlinear phenomena and complex systems C.P. 231, Blvd. du Triomphe, 1050 Brussels, Belgium

(Received 21 August 2003; accepted in final form 12 February 2004)

The effects arising from the presence of a ramp and of a stochastic forcing on a limit point bifurcation are analyzed. It is shown that in a noise-free system the presence of a ramp induces the stabilization of states that would otherwise show explosive behavior. When noise is switched on, the system becomes frozen on a stable configuration with some probability which depends on the rate of the ramp, the strength of the noise and the initial condition.

05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
05.10.Gg - Stochastic analysis methods (Fokker-Planck, Langevin, etc.).
05.45.-a - Nonlinear dynamics and nonlinear dynamical systems.

© EDP Sciences 2004