Robust chaos in a totally symmetric network of four phase oscillators
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929457252532224 |
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| author | Karatetskaia, Efrosiniia Kazakov, Alexey Safonov, Klim Turaev, Dmitry |
| author_facet | Karatetskaia, Efrosiniia Kazakov, Alexey Safonov, Klim Turaev, Dmitry |
| contents | We provide conditions on the coupling function such that a system of 4 globally coupled identical oscillators has chaotic attractors, a pair of Lorenz attractors or a 4-winged analogue of the Lorenz attractor. The attractors emerge near the triple instability threshold of the splay-phase synchronization state of the oscillators. We provide theoretical arguments and verify numerically, based on the pseudohyperbolicity test, that the chaotic dynamics are robust with respect to small, e.g. time-dependent, perturbations of the system. The robust chaoticity should also be inherited by any network of weakly interacting systems with such attractors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06435 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust chaos in a totally symmetric network of four phase oscillators Karatetskaia, Efrosiniia Kazakov, Alexey Safonov, Klim Turaev, Dmitry Chaotic Dynamics Dynamical Systems We provide conditions on the coupling function such that a system of 4 globally coupled identical oscillators has chaotic attractors, a pair of Lorenz attractors or a 4-winged analogue of the Lorenz attractor. The attractors emerge near the triple instability threshold of the splay-phase synchronization state of the oscillators. We provide theoretical arguments and verify numerically, based on the pseudohyperbolicity test, that the chaotic dynamics are robust with respect to small, e.g. time-dependent, perturbations of the system. The robust chaoticity should also be inherited by any network of weakly interacting systems with such attractors. |
| title | Robust chaos in a totally symmetric network of four phase oscillators |
| topic | Chaotic Dynamics Dynamical Systems |
| url | https://arxiv.org/abs/2408.06435 |