Topological synchronisation or a simple attractor?
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| Title: | Topological synchronisation or a simple attractor? |
|---|---|
| Authors: | Caby, Théophile, Gianfelice, Michele, Saussol, Benoît, Vaienti, Sandro |
| Contributors: | Caby, Théophile |
| Source: | Nonlinearity. 36:3603-3621 |
| Publication Status: | Preprint |
| Publisher Information: | IOP Publishing, 2023. |
| Publication Year: | 2023 |
| Subject Terms: | 0301 basic medicine, 03 medical and health sciences, [NLIN.NLIN-CD] Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD], 0103 physical sciences, FOS: Mathematics, [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], topological synchronization, dynamical systems, unimodal maps, master slave system, generalized dimensions, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, 0101 mathematics, 01 natural sciences |
| Description: | A few recent papers introduced the concept of topological synchronisation. We refer in particular to (Lahav et al 2022 Sci. Rep. 12 2508), where the theory was illustrated by means of a skew product system, coupling two logistic maps. In this case, we show that the topological synchronisation could be easily explained as the birth of an attractor for increasing values of the coupling strength and the mutual convergence of two marginal empirical measures. Numerical computations based on a careful analysis of the Lyapunov exponents suggest that the attractor supports an absolutely continuous physical measure (acpm). We finally show that for some unimodal maps such acpm exhibit a multifractal structure. |
| Document Type: | Article |
| File Description: | application/pdf |
| ISSN: | 1361-6544 0951-7715 |
| DOI: | 10.1088/1361-6544/acd42f |
| DOI: | 10.48550/arxiv.2210.07941 |
| Access URL: | http://arxiv.org/abs/2210.07941 |
| Rights: | CC BY |
| Accession Number: | edsair.doi.dedup.....937a21f185631be8b816e377bd403702 |
| Database: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstract: | A few recent papers introduced the concept of topological synchronisation. We refer in particular to (Lahav et al 2022 Sci. Rep. 12 2508), where the theory was illustrated by means of a skew product system, coupling two logistic maps. In this case, we show that the topological synchronisation could be easily explained as the birth of an attractor for increasing values of the coupling strength and the mutual convergence of two marginal empirical measures. Numerical computations based on a careful analysis of the Lyapunov exponents suggest that the attractor supports an absolutely continuous physical measure (acpm). We finally show that for some unimodal maps such acpm exhibit a multifractal structure. |
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| ISSN: | 13616544 09517715 |
| DOI: | 10.1088/1361-6544/acd42f |