Noise-induced Statistical Periodicity in Random Lasota-Mackey Maps

TL;DR

This paper investigates how noise can induce statistical periodicity in one-dimensional maps, specifically in a modified Lasota-Mackey map, revealing a transition from stable to periodic density states influenced by noise levels.

Contribution

It demonstrates the existence of noise-induced statistical periodicity in a modified Lasota-Mackey map and explains it through almost cyclic sets and a transfer operator approach.

Findings

Existence of statistical periodicity in the modified Lasota-Mackey map.

Transition from stable to periodic density states with increasing noise.

Statistical periodicity as the origin of almost periodicity in noise-induced order.

Abstract

Noise-induced statistical periodicity in a class of one-dimensional maps is studied. We show the existence of statistical periodicity in a modified Lasota-Mackey map and describe the phenomenon in terms of almost cyclic sets. A transition from a stable state to a periodic state of the density depending on the noise level is observed in numerical investigations based on trajectory averages and by means of a transfer operator approach. We conclude that the statistical periodicity is the origin of the almost periodicity in noise-induced order.