Global Topological Dirac Synchronization
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866908603912290304 |
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| author | Carletti, Timoteo Giambagli, Lorenzo Muolo, Riccardo Bianconi, Ginestra |
| author_facet | Carletti, Timoteo Giambagli, Lorenzo Muolo, Riccardo Bianconi, Ginestra |
| contents | Synchronization is a fundamental dynamical state of interacting oscillators, observed in natural biological rhythms and in the brain. Global synchronization which occurs when non-linear or chaotic oscillators placed on the nodes of a network display the same dynamics as received great attention in network theory. Here we propose and investigate Global Topological Dirac Synchronization on higher-order networks such as cell and simplicial complexes. This is a state where oscillators associated to simplices and cells of arbitrary dimension, coupled by the Topological Dirac operator, operate at unison. By combining algebraic topology with non-linear dynamics and machine learning, we derive the topological conditions under which this state exists and the dynamical conditions under which it is stable. We provide evidence of 1-dimensional simplicial complexes (networks) and 2-dimensional simplicial and cell complexes where Global Topological Dirac Synchronization can be observed. Our results point out that Global Topological Dirac Synchronization is a possible dynamical state of simplicial and cell complexes that occur only in some specific network topologies and geometries, the latter ones being determined by the weights of the higher-order networks |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15338 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global Topological Dirac Synchronization Carletti, Timoteo Giambagli, Lorenzo Muolo, Riccardo Bianconi, Ginestra Statistical Mechanics Disordered Systems and Neural Networks Mathematical Physics Dynamical Systems Adaptation and Self-Organizing Systems Synchronization is a fundamental dynamical state of interacting oscillators, observed in natural biological rhythms and in the brain. Global synchronization which occurs when non-linear or chaotic oscillators placed on the nodes of a network display the same dynamics as received great attention in network theory. Here we propose and investigate Global Topological Dirac Synchronization on higher-order networks such as cell and simplicial complexes. This is a state where oscillators associated to simplices and cells of arbitrary dimension, coupled by the Topological Dirac operator, operate at unison. By combining algebraic topology with non-linear dynamics and machine learning, we derive the topological conditions under which this state exists and the dynamical conditions under which it is stable. We provide evidence of 1-dimensional simplicial complexes (networks) and 2-dimensional simplicial and cell complexes where Global Topological Dirac Synchronization can be observed. Our results point out that Global Topological Dirac Synchronization is a possible dynamical state of simplicial and cell complexes that occur only in some specific network topologies and geometries, the latter ones being determined by the weights of the higher-order networks |
| title | Global Topological Dirac Synchronization |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Mathematical Physics Dynamical Systems Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2410.15338 |