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arXiv · 2403.13116

Noisy Fixed Points: Stability of the Invariant Distribution of the Random Logistic Map

Kimberly Ayers·Ami Radunskaya
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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.

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Kimberly Ayers, Ami Radunskaya. 2024-03-19. Noisy Fixed Points: Stability of the Invariant Distribution of the Random Logistic Map. https://arxiv.org/abs/2403.13116

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