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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.

Keywords

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}
}