Existence of multiple noise-induced transitions in Lasota–Mackey maps

We prove the existence of multiple noise-induced transitions in the Lasota–Mackey map, which is a class of one-dimensional random dynamical system with additive noise. The result is achieved with the help of rigorous computer assisted estimates. We first approximate the stationary distribution of th...

Full description

Saved in:
Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2022-01, Vol.32 (1), p.013117-013117
Main Authors: Chihara, Takumi, Sato, Yuzuru, Nisoli, Isaia, Galatolo, Stefano
Format: Article
Language:English
Subjects:
Dynamical systems
Liapunov exponents
Noise
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove the existence of multiple noise-induced transitions in the Lasota–Mackey map, which is a class of one-dimensional random dynamical system with additive noise. The result is achieved with the help of rigorous computer assisted estimates. We first approximate the stationary distribution of the random dynamical system and then compute certified error intervals for the Lyapunov exponent. We find that the sign of the Lyapunov exponent changes at least three times when increasing the noise amplitude. We also show numerical evidence that the standard non-rigorous numerical approximation by finite-time Lyapunov exponent is valid with our model for a sufficiently large number of iterations. Our method is expected to work for a broad class of nonlinear stochastic phenomena.
ISSN:1054-1500
1089-7682
DOI:10.1063/5.0070198