Möbius group actions in the solvable chimera model
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866929485229588480 |
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| author | Jaćimović, Vladimir Crnkić, Aladin |
| author_facet | Jaćimović, Vladimir Crnkić, Aladin |
| contents | We study actions of Möbius group on two sub-populations in the solvable chimera model proposed by Abrams et al. Dynamics of global variables are given by two coupled Watanabe-Strogatz systems, one for each sub-population.
At the first glance, asymptotic dynamics in the model seem to be very simple. For instance, in the stable chimera state distributions of oscillators perform a simple rotations after a certain (sufficiently large) moment. However, a closer look unveils that dynamics are subtler that what can be observed from evolution of densities of oscillators' phases. In order to gain the full picture, one needs to investigate dynamics on the transformation group that acts on these densities. Such an approach emphasizes impact of the "hidden" variable that is not visible on macroscopic level. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2110_14697 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Möbius group actions in the solvable chimera model Jaćimović, Vladimir Crnkić, Aladin Adaptation and Self-Organizing Systems Dynamical Systems Chaotic Dynamics Pattern Formation and Solitons We study actions of Möbius group on two sub-populations in the solvable chimera model proposed by Abrams et al. Dynamics of global variables are given by two coupled Watanabe-Strogatz systems, one for each sub-population. At the first glance, asymptotic dynamics in the model seem to be very simple. For instance, in the stable chimera state distributions of oscillators perform a simple rotations after a certain (sufficiently large) moment. However, a closer look unveils that dynamics are subtler that what can be observed from evolution of densities of oscillators' phases. In order to gain the full picture, one needs to investigate dynamics on the transformation group that acts on these densities. Such an approach emphasizes impact of the "hidden" variable that is not visible on macroscopic level. |
| title | Möbius group actions in the solvable chimera model |
| topic | Adaptation and Self-Organizing Systems Dynamical Systems Chaotic Dynamics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2110.14697 |