R. Wackerbauer, NOISE-INDUCED STABILIZATION OF ONE-DIMENSIONAL DISCONTINUOUS MAPS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 58(3), 1998, pp. 3036-3044
Dynamical noise yields a stabilization, or switching inertia, of the f
lip-flop process in the Lorenz flow [R. Wackerbauer. Phys. Rev. E 52,
4745 (1995)]. In order to understand the corresponding stabilization m
echanisms in general, a systematic analysis of the influence of dynami
cal perturbations on the switching process of one-dimensional, discont
inuous maps (a piecewise linear map, a Lorenz map, and a piecewise lin
ear Lorenz approximation) is presented. It turns out that the dominant
stabilization mechanism in all Lorenz-type maps under study is caused
by a noise-induced unstable fixed point, resulting in a noise-induced
escape of a typical trajectory into a less frequently visited part of
the attractor.