Kuramoto Oscillators With Asymmetric Coupling
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917815819173888 |
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| author | Sander, Leonard M. |
| author_facet | Sander, Leonard M. |
| contents | We study a system of coupled oscillators of the Sakaguchi-Kuramoto type with interactions including a phase delay. We consider the case of a coupling matrix such that oscillators with large natural frequencies drive all slower ones but not the reverse. This scheme is inspired by Hebbian learning in neuroscience. We propose a simple model which is partly solvable analytically and shows many unusual features. For example, for the case of phase delay $π/2$ (a symmetric phase response curve) with symmetric coupling there is no synchronous behavior. But in the asymmetric coupling case, there are phase-locked states, i.e., states where many oscillators have the same frequency, but with substantial phase differences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19156 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kuramoto Oscillators With Asymmetric Coupling Sander, Leonard M. Adaptation and Self-Organizing Systems Neurons and Cognition We study a system of coupled oscillators of the Sakaguchi-Kuramoto type with interactions including a phase delay. We consider the case of a coupling matrix such that oscillators with large natural frequencies drive all slower ones but not the reverse. This scheme is inspired by Hebbian learning in neuroscience. We propose a simple model which is partly solvable analytically and shows many unusual features. For example, for the case of phase delay $π/2$ (a symmetric phase response curve) with symmetric coupling there is no synchronous behavior. But in the asymmetric coupling case, there are phase-locked states, i.e., states where many oscillators have the same frequency, but with substantial phase differences. |
| title | Kuramoto Oscillators With Asymmetric Coupling |
| topic | Adaptation and Self-Organizing Systems Neurons and Cognition |
| url | https://arxiv.org/abs/2410.19156 |