Scaling Law for Characteristic Times of Noise-Induced Crises

We consider the influence of random noise on low-dimensional, nonlinear dynamical systems with parameters near values leading to a crisis in the absence of noise.

 A previous analysis of the noisy logistic map [F. T. Arecchi, R. Badii, and A. Politi, Phys. Lett. 103A, 3 (1984)] is shown to be consistent with our general result. Illustrative numerical examples are given for two-dimensional maps and a three-dimensional flow. In addition, the relevance of the noise scaling law to experimental situations is discussed.