Conservative dynamics in phase oscillator networks
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908915688538112 |
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| author | Pikovsky, Arkady |
| author_facet | Pikovsky, Arkady |
| contents | The interaction between phase oscillators is conservative if the phase volume is conserved throughout the dynamics. We derive a general condition, based on the notion of a pair-Hamiltonian, for the pairwise couplings to be conservative. The conservative networks with Winfree-type and Kuramoto-Daido-type couplings are also discussed. It is demonstrated that although, in contradistinction to genuine Hamiltonian dynamics, there is no exact pairwise symmetry of the Lyapunov exponents, the Lyapunov spectrum for a large network is nearly symmetric. The concept is also generalized to triplet and quadruplet couplings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25431 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conservative dynamics in phase oscillator networks Pikovsky, Arkady Chaotic Dynamics Adaptation and Self-Organizing Systems The interaction between phase oscillators is conservative if the phase volume is conserved throughout the dynamics. We derive a general condition, based on the notion of a pair-Hamiltonian, for the pairwise couplings to be conservative. The conservative networks with Winfree-type and Kuramoto-Daido-type couplings are also discussed. It is demonstrated that although, in contradistinction to genuine Hamiltonian dynamics, there is no exact pairwise symmetry of the Lyapunov exponents, the Lyapunov spectrum for a large network is nearly symmetric. The concept is also generalized to triplet and quadruplet couplings. |
| title | Conservative dynamics in phase oscillator networks |
| topic | Chaotic Dynamics Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2603.25431 |