Noise-induced stabilization of one-dimensional discontinuous maps

Dynamical noise yields a stabilization, or switching inertia, of the flip-flop process in the Lorenz flow [R. Wackerbauer, Phys. Rev. E 52, 4745 (1995)]. In order to understand the corresponding stabilization mechanisms in general, a systematic analysis of the influence of dynamical perturbations on the switching process of one-dimensional, discontinuous maps (a piecewise linear map, a Lorenz map, and a piecewise linear 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.