Noisy Fixed Points: Stability of the Invariant Distribution of the Random Logistic Map
Kimberly Ayers, Ami Radunskaya
Published: 2024/3/19
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.