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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.13116 |
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| _version_ | 1866909773000081408 |
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| author | Ayers, Kimberly Radunskaya, Ami |
| author_facet | Ayers, Kimberly Radunskaya, Ami |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13116 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Noisy Fixed Points: Stability of the Invariant Distribution of the Random Logistic Map Ayers, Kimberly Radunskaya, Ami Dynamical Systems 37 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. |
| title | Noisy Fixed Points: Stability of the Invariant Distribution of the Random Logistic Map |
| topic | Dynamical Systems 37 |
| url | https://arxiv.org/abs/2403.13116 |