Extraordinarily superpersistent chaotic transientsYounghae 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: , where C0, C1, and are positive constants and is a scaling parameter. This occurs in dynamical systems preceding an unstable-unstable pair bifurcation, subject to noise of amplitude . The extreme longevity of the transient lifetime for small 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