Europhys. Lett.
Volume 67, Number 6, September 2004
Page(s) 914 - 920
Section General
Published online 01 September 2004
Europhys. Lett., 67 (6), pp. 914-920 (2004)
DOI: 10.1209/epl/i2004-10142-5

Extraordinarily superpersistent chaotic transients

Younghae Do1 and Ying-Cheng Lai1, 2

1  Department of Mathematics, Arizona State University - Tempe, AZ 85287, USA
2  Departments of Electrical Engineering and Physics, Arizona State University Tempe, AZ 85287, USA

(Received 7 June 2004; accepted in final form 8 July 2004)

We uncovered a class of transient chaos for which the average lifetime obeys the following scaling law: $\tau\sim\exp[C_0\exp[C_1\varepsilon^{-\gamma}]]$, where C0, C1, and $\gamma$ are positive constants and $\varepsilon$ is a scaling parameter. This occurs in dynamical systems preceding an unstable-unstable pair bifurcation, subject to noise of amplitude $\varepsilon$. The extreme longevity of the transient lifetime for small $\varepsilon$ is striking, which has not been reported previously. We formulate a theory to explain this type of extraordinarily superpersistent chaotic transients, and point out physical relevance and implications.

05.45.-a - Nonlinear dynamics and nonlinear dynamical systems.
05.10.Gg - Stochastic analysis methods (Fokker-Planck, Langevin, etc.).

© EDP Sciences 2004