Global Topological Dirac Synchronization
Synchronization is a fundamental dynamical state of interacting oscillators, observed, e.g., 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 has received great attent...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2025-01-01
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| Series: | Journal of Physics: Complexity |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/2632-072X/add0fe |
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| Summary: | Synchronization is a fundamental dynamical state of interacting oscillators, observed, e.g., 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 has received great attention in network theory. Here we propose and investigate Global Topological Dirac Synchronization (GTDS) 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 GTDS can be observed. Our results point out that GTDS is a possible dynamical state of cell complexes and simplicial complexes that occur only in some specific network topologies and geometries, the latter ones being determined by the weights of the higher-order networks. |
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| ISSN: | 2632-072X |