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arXiv · 2409.07546

Localized synchronous patterns in weakly coupled bistable oscillators

Erik Bergland·Jason J Bramburger·Bjorn Sandstede
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Abstract

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.

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Erik Bergland, Jason J Bramburger, Bjorn Sandstede. 2024-09-11. Localized synchronous patterns in weakly coupled bistable oscillators. https://doi.org/10.1016/j.physd.2025.134537

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