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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.14646 |
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| _version_ | 1866908456894595072 |
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| author | Zhang, Junke Wang, Yiqian |
| author_facet | Zhang, Junke Wang, Yiqian |
| contents | The coupled (chaotic) map lattices (CMLs) characterizes the collective dynamics of a spatially distributed system consisting of locally or globally coupled maps. The current research on the dynamic behavior of CMLs is based on the framework of the Perron-Frobenius operator and mainly focuses on weakly-coupled cases. In this paper, a novel geometric-combinatorics method for for non weakly-coupled CMLs is provided on the dynamical behavior of a two-node CMLs with identical piecewise linear expanding maps. We obtain a necessary-sufficient condition for the uniqueness of absolutely continuous invariant measure (ACIM) and for the occurrence of intermittent-synchronization, that is, almost each orbit enters and exits an arbitrarily small neighborhood of the diagonal for an infinite number of times. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14646 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intermittent--synchronization in non-weakly coupled piecewise linear expanding map lattice: a geometric-combinatorics method Zhang, Junke Wang, Yiqian Dynamical Systems 37A05, 37A10 The coupled (chaotic) map lattices (CMLs) characterizes the collective dynamics of a spatially distributed system consisting of locally or globally coupled maps. The current research on the dynamic behavior of CMLs is based on the framework of the Perron-Frobenius operator and mainly focuses on weakly-coupled cases. In this paper, a novel geometric-combinatorics method for for non weakly-coupled CMLs is provided on the dynamical behavior of a two-node CMLs with identical piecewise linear expanding maps. We obtain a necessary-sufficient condition for the uniqueness of absolutely continuous invariant measure (ACIM) and for the occurrence of intermittent-synchronization, that is, almost each orbit enters and exits an arbitrarily small neighborhood of the diagonal for an infinite number of times. |
| title | Intermittent--synchronization in non-weakly coupled piecewise linear expanding map lattice: a geometric-combinatorics method |
| topic | Dynamical Systems 37A05, 37A10 |
| url | https://arxiv.org/abs/2507.14646 |