Network and Phase Symmetries Reveal That Amplitude Dynamics Stabilize Decoupled Oscillator Clusters
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network’s automorphism group, we explore synchronization patterns that emerge from the phas...
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MDPI AG
2025-05-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/27/5/501 |
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| author | Jeffrey Emenheiser Anastasiya Salova Jordan Snyder James P. Crutchfield Raissa M. D’Souza |
| author_facet | Jeffrey Emenheiser Anastasiya Salova Jordan Snyder James P. Crutchfield Raissa M. D’Souza |
| author_sort | Jeffrey Emenheiser |
| collection | DOAJ |
| description | Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network’s automorphism group, we explore synchronization patterns that emerge from the phase-shift invariance of the dynamical equations and symmetries in the nodes. We show that these nonstructural symmetries simplify stability calculations. We analyze a ring-network of phase–amplitude oscillators that exhibits a “decoupled” state in which physically-coupled nodes appear to act independently due to emergent cancellations in the equations of dynamical evolution. We establish that this state can be linearly stable for a ring of phase–amplitude oscillators, but not for a ring of phase-only oscillators that otherwise require explicit long-range, nonpairwise, or nonphase coupling. In short, amplitude–phase interactions are key to stable synchronization at a distance. |
| format | Article |
| id | doaj-art-e9fea30ae0504965bfaff847ab70ce12 |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-e9fea30ae0504965bfaff847ab70ce122025-08-20T03:47:52ZengMDPI AGEntropy1099-43002025-05-0127550110.3390/e27050501Network and Phase Symmetries Reveal That Amplitude Dynamics Stabilize Decoupled Oscillator ClustersJeffrey Emenheiser0Anastasiya Salova1Jordan Snyder2James P. Crutchfield3Raissa M. D’Souza4Complexity Sciences Center and Physics, Mathematics, and Computer Science Departments, University of California, Davis, One Shields Avenue, Davis, CA 95616, USAComplexity Sciences Center and Physics, Mathematics, and Computer Science Departments, University of California, Davis, One Shields Avenue, Davis, CA 95616, USAComplexity Sciences Center and Physics, Mathematics, and Computer Science Departments, University of California, Davis, One Shields Avenue, Davis, CA 95616, USAComplexity Sciences Center and Physics, Mathematics, and Computer Science Departments, University of California, Davis, One Shields Avenue, Davis, CA 95616, USAComplexity Sciences Center and Physics, Mathematics, and Computer Science Departments, University of California, Davis, One Shields Avenue, Davis, CA 95616, USAOscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network’s automorphism group, we explore synchronization patterns that emerge from the phase-shift invariance of the dynamical equations and symmetries in the nodes. We show that these nonstructural symmetries simplify stability calculations. We analyze a ring-network of phase–amplitude oscillators that exhibits a “decoupled” state in which physically-coupled nodes appear to act independently due to emergent cancellations in the equations of dynamical evolution. We establish that this state can be linearly stable for a ring of phase–amplitude oscillators, but not for a ring of phase-only oscillators that otherwise require explicit long-range, nonpairwise, or nonphase coupling. In short, amplitude–phase interactions are key to stable synchronization at a distance.https://www.mdpi.com/1099-4300/27/5/501synchronizationphase-amplitude oscillatorcluster stabilitycollective behavioremergent symmetriesphase shift |
| spellingShingle | Jeffrey Emenheiser Anastasiya Salova Jordan Snyder James P. Crutchfield Raissa M. D’Souza Network and Phase Symmetries Reveal That Amplitude Dynamics Stabilize Decoupled Oscillator Clusters Entropy synchronization phase-amplitude oscillator cluster stability collective behavior emergent symmetries phase shift |
| title | Network and Phase Symmetries Reveal That Amplitude Dynamics Stabilize Decoupled Oscillator Clusters |
| title_full | Network and Phase Symmetries Reveal That Amplitude Dynamics Stabilize Decoupled Oscillator Clusters |
| title_fullStr | Network and Phase Symmetries Reveal That Amplitude Dynamics Stabilize Decoupled Oscillator Clusters |
| title_full_unstemmed | Network and Phase Symmetries Reveal That Amplitude Dynamics Stabilize Decoupled Oscillator Clusters |
| title_short | Network and Phase Symmetries Reveal That Amplitude Dynamics Stabilize Decoupled Oscillator Clusters |
| title_sort | network and phase symmetries reveal that amplitude dynamics stabilize decoupled oscillator clusters |
| topic | synchronization phase-amplitude oscillator cluster stability collective behavior emergent symmetries phase shift |
| url | https://www.mdpi.com/1099-4300/27/5/501 |
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