Analytical foundation for adversarial synchronization control in oscillator networks
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917546336190464 |
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| author | Takemoto, Kazuhiro |
| author_facet | Takemoto, Kazuhiro |
| contents | This study provides an analytical foundation for adversarial synchronization control in Kuramoto oscillator networks, where small gradient-based perturbations applied repeatedly to oscillator phases can dramatically enhance or suppress collective synchronization. Using the Ott--Antonsen reduction, we derive an exact closed-form expression for the effect of a single adversarial perturbation (kick) on the order parameter. A key finding is that each kick produces a finite, coupling-independent increment in the order parameter even when synchronization is arbitrarily weak, which combined with slow relaxation near the critical coupling and mean-field feedback explains the disproportionate amplification previously observed in numerical simulations. Fixed-point analysis further reveals a fundamental asymmetry between enhancement and suppression, with the latter governed by noise-induced escape in finite systems. Extending the framework to networks via the annealed network approximation, we show that the theory captures the synchronization behavior of representative model networks and identify a decoupling between kick sensitivity and mean-field dominance in scale-free networks. These results offer a tractable theoretical basis for understanding and designing kick-based synchronization control in oscillator networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14492 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Analytical foundation for adversarial synchronization control in oscillator networks Takemoto, Kazuhiro Adaptation and Self-Organizing Systems Physics and Society This study provides an analytical foundation for adversarial synchronization control in Kuramoto oscillator networks, where small gradient-based perturbations applied repeatedly to oscillator phases can dramatically enhance or suppress collective synchronization. Using the Ott--Antonsen reduction, we derive an exact closed-form expression for the effect of a single adversarial perturbation (kick) on the order parameter. A key finding is that each kick produces a finite, coupling-independent increment in the order parameter even when synchronization is arbitrarily weak, which combined with slow relaxation near the critical coupling and mean-field feedback explains the disproportionate amplification previously observed in numerical simulations. Fixed-point analysis further reveals a fundamental asymmetry between enhancement and suppression, with the latter governed by noise-induced escape in finite systems. Extending the framework to networks via the annealed network approximation, we show that the theory captures the synchronization behavior of representative model networks and identify a decoupling between kick sensitivity and mean-field dominance in scale-free networks. These results offer a tractable theoretical basis for understanding and designing kick-based synchronization control in oscillator networks. |
| title | Analytical foundation for adversarial synchronization control in oscillator networks |
| topic | Adaptation and Self-Organizing Systems Physics and Society |
| url | https://arxiv.org/abs/2605.14492 |