Equitability and explosive synchronisation in multiplex and higher-order networks
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909963774853120 |
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| author | Kovalenko, Kirill Contreras-Aso, Gonzalo del Genio, Charo I. Boccaletti, Stefano Sánchez-García, Rubén J. |
| author_facet | Kovalenko, Kirill Contreras-Aso, Gonzalo del Genio, Charo I. Boccaletti, Stefano Sánchez-García, Rubén J. |
| contents | Cluster synchronisation is a key phenomenon observed in networks of coupled dynamical units. Its presence has been linked to symmetry and, more generally, to equability of the underlying pattern of interactions between dynamical units. However, it is not known under which conditions equitability-induced synchronisation is the only cluster synchronisation that can occur on a particular system. Here, we reveal a natural linear independent condition such that equitability becomes necessary, and sufficient, for the existence of cluster synchronised solutions on a very general dynamical system which allows multiplex or higher-order, arbitrarily weighted interactions. Our results explain the ubiquity of explosive synchronisation, as opposed to cluster synchronisation, in multiplex and higher-order networks: equitability imposes additional constraints that must be simultaneously satisfied on the same set of nodes. Our results have significant implications for the design of complex dynamical systems of coupled dynamical units with arbitrary cluster synchronisation patterns and coupling functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09319 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equitability and explosive synchronisation in multiplex and higher-order networks Kovalenko, Kirill Contreras-Aso, Gonzalo del Genio, Charo I. Boccaletti, Stefano Sánchez-García, Rubén J. Adaptation and Self-Organizing Systems Dynamical Systems Cluster synchronisation is a key phenomenon observed in networks of coupled dynamical units. Its presence has been linked to symmetry and, more generally, to equability of the underlying pattern of interactions between dynamical units. However, it is not known under which conditions equitability-induced synchronisation is the only cluster synchronisation that can occur on a particular system. Here, we reveal a natural linear independent condition such that equitability becomes necessary, and sufficient, for the existence of cluster synchronised solutions on a very general dynamical system which allows multiplex or higher-order, arbitrarily weighted interactions. Our results explain the ubiquity of explosive synchronisation, as opposed to cluster synchronisation, in multiplex and higher-order networks: equitability imposes additional constraints that must be simultaneously satisfied on the same set of nodes. Our results have significant implications for the design of complex dynamical systems of coupled dynamical units with arbitrary cluster synchronisation patterns and coupling functions. |
| title | Equitability and explosive synchronisation in multiplex and higher-order networks |
| topic | Adaptation and Self-Organizing Systems Dynamical Systems |
| url | https://arxiv.org/abs/2507.09319 |