Noisy Fixed Points: Stability of the Invariant Distribution of the Random Logistic Map
Dynamical Systems
2025-09-09 v4
Abstract
The full family of discrete logistic maps has been widely studied both as a canonical example of the period-doubling route to chaos, and as a model of natural processes. In this paper we present a study of the stochastic process described by iterations of the logistic map with a random parameter. In addition to bringing together previously known results, we present a proof that the unique invariant measure of the process in the chaotic regime is asymptotically stable.
Cite
@article{arxiv.2403.13116,
title = {Noisy Fixed Points: Stability of the Invariant Distribution of the Random Logistic Map},
author = {Kimberly Ayers and Ami Radunskaya},
journal= {arXiv preprint arXiv:2403.13116},
year = {2025}
}