Localized synchronous patterns in weakly coupled bistable oscillators
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915823742877696 |
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| author | Bergland, Erik Bramburger, Jason J Sandstede, Bjorn |
| author_facet | Bergland, Erik Bramburger, Jason J Sandstede, Bjorn |
| contents | Motivated by numerical continuation studies of coupled mechanical oscillators, we investigate branches of localized time-periodic solutions of one-dimensional chains of coupled oscillators. We focus on Ginzburg--Landau equations with nonlinearities of Lambda-Omega type and establish the existence of localized synchrony patterns in the case of weak coupling and weak-amplitude dependence of the oscillator periods. Depending on the coupling, localized synchrony patterns lie on a discrete stack of isola branches or on a single connected snaking branch. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_07546 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Localized synchronous patterns in weakly coupled bistable oscillators Bergland, Erik Bramburger, Jason J Sandstede, Bjorn Dynamical Systems Pattern Formation and Solitons 37G15, 37L60, 34C37 Motivated by numerical continuation studies of coupled mechanical oscillators, we investigate branches of localized time-periodic solutions of one-dimensional chains of coupled oscillators. We focus on Ginzburg--Landau equations with nonlinearities of Lambda-Omega type and establish the existence of localized synchrony patterns in the case of weak coupling and weak-amplitude dependence of the oscillator periods. Depending on the coupling, localized synchrony patterns lie on a discrete stack of isola branches or on a single connected snaking branch. |
| title | Localized synchronous patterns in weakly coupled bistable oscillators |
| topic | Dynamical Systems Pattern Formation and Solitons 37G15, 37L60, 34C37 |
| url | https://arxiv.org/abs/2409.07546 |