Extraordinarily superpersistent chaotic transients

We uncovered a class of transient chaos for which the average lifetime obeys the following scaling law: τ ∼ exp[C₀ exp[C ₁ε^-γ]], where C₀, C₁, and γ are positive constants and ε is a scaling parameter. This occurs in dynamical systems preceding an unstable-unstable pair bifurcation, subject to noise of amplitude ε. The extreme longevity of the transient lifetime for small ε 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.