Noise-induced Statistical Periodicity in Random Lasota-Mackey Maps

2019/05/07 by Sato, Yuzuru, Padberg-Gehle, Kathrin
#Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences

paper · doi:10.48550/arxiv.1905.02746

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.

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