A note on the topological synchronization of unimodal maps
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| Title: | A note on the topological synchronization of unimodal maps |
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| Authors: | Michele Gianfelice |
| Source: | Nonlinearity. 38:015007 |
| Publication Status: | Preprint |
| Publisher Information: | IOP Publishing, 2024. |
| Publication Year: | 2024 |
| Subject Terms: | coupled dynamical systems, unimodal maps, master-slave system, Markov chains, random dynamical systems, topological synchronisation, 37A10, 60J10, Probability (math.PR), FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, 0101 mathematics, 01 natural sciences, Mathematics - Probability |
| Description: | In this note we complete the analysis carried on in Caby et al (2023 Nonlinearity 36 3603–21) about the topological synchronisation of unimodal maps of the interval coupled in a master–slave configuration, by answering to the questions raised in that Paper. Namely, we compute the weak limits of the invariant measure of the coupled system as the coupling strength k ∈ ( 0 , 1 ) tends to 0 and to 1 and discuss the uniqueness of the invariant measure of its random dynamical system counterpart, proving that the convergence of the associated Markov chain to its unique stationary measure is geometric. |
| Document Type: | Article |
| ISSN: | 1361-6544 0951-7715 |
| DOI: | 10.1088/1361-6544/ad95d5 |
| DOI: | 10.48550/arxiv.2405.07661 |
| Access URL: | http://arxiv.org/abs/2405.07661 |
| Rights: | CC BY arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....dea384b42ffc061d127de629fa2f13f1 |
| Database: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstract: | In this note we complete the analysis carried on in Caby et al (2023 Nonlinearity 36 3603–21) about the topological synchronisation of unimodal maps of the interval coupled in a master–slave configuration, by answering to the questions raised in that Paper. Namely, we compute the weak limits of the invariant measure of the coupled system as the coupling strength k ∈ ( 0 , 1 ) tends to 0 and to 1 and discuss the uniqueness of the invariant measure of its random dynamical system counterpart, proving that the convergence of the associated Markov chain to its unique stationary measure is geometric. |
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| ISSN: | 13616544 09517715 |
| DOI: | 10.1088/1361-6544/ad95d5 |