Global Phase Synchronization Decoupled from Amplitude Dynamics
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915708108013568 |
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| author | Yawata, Koichiro Nakao, Hiroya |
| author_facet | Yawata, Koichiro Nakao, Hiroya |
| contents | The Kuramoto model is a canonical framework for analyzing phase synchronization, yet its utility is restricted to the vicinity of the oscillator's unperturbed limit cycle. Here, we present a method to construct coupled-oscillator models that globally preserve Kuramoto-type phase dynamics by using phase-amplitude coordinates defined via Koopman operator theory. We introduce a solvable model, termed Kuramoto-Stuart-Landau model, which exhibits nontrivial synchronized dynamics far from the limit cycle. We also construct three phase synchronized oscillators whose amplitudes exhibit Lorenz-type chaos. Our method is applicable to general limit-cycle systems, achieving phase synchronization globally while preserving arbitrarily complex amplitude dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01919 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global Phase Synchronization Decoupled from Amplitude Dynamics Yawata, Koichiro Nakao, Hiroya Adaptation and Self-Organizing Systems Chaotic Dynamics The Kuramoto model is a canonical framework for analyzing phase synchronization, yet its utility is restricted to the vicinity of the oscillator's unperturbed limit cycle. Here, we present a method to construct coupled-oscillator models that globally preserve Kuramoto-type phase dynamics by using phase-amplitude coordinates defined via Koopman operator theory. We introduce a solvable model, termed Kuramoto-Stuart-Landau model, which exhibits nontrivial synchronized dynamics far from the limit cycle. We also construct three phase synchronized oscillators whose amplitudes exhibit Lorenz-type chaos. Our method is applicable to general limit-cycle systems, achieving phase synchronization globally while preserving arbitrarily complex amplitude dynamics. |
| title | Global Phase Synchronization Decoupled from Amplitude Dynamics |
| topic | Adaptation and Self-Organizing Systems Chaotic Dynamics |
| url | https://arxiv.org/abs/2601.01919 |