Conservative dynamics in phase oscillator networks

2026/03/26 by Arkady Pikovsky · 1 voice
Physics and Astronomy · #nlin.AO #nlin.CD

paper · pdf · doi:10.1088/2632-072x/ae669b

Abstract

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.

Citations

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Discussions

• Arkady Pikovsky: Conservative dynamics in phase oscillator networks https://arxiv.org/abs/2603.25431 https://arxiv.org/pdf/2603.25431 https://arxiv.org/html/2603.25431 [bsky, 0 points, 0 comments]

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