Extraordinarily superpersistent chaotic transients

We uncovered a class of transient chaos for which the average lifetime obeys the following scaling law: tau similar to exp[C-0 exp[C(1)epsilon(-gamma)]], where C-0, C-1, and gamma are positive constants and epsilon is a scaling parameter. This occurs in dynamical systems preceding an unstable-unstable pair bifurcation, subject to noise of amplitude epsilon. The extreme longevity of the transient lifetime for small epsilon 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.