Localized synchronous patterns in weakly coupled bistable oscillators

2024/09/11 by Erik Bergland, Bergland, Erik, Jason J. Bramburger +3 · 1 citation
Computer Science · Physics and Astronomy · #34C37 #37G15 #37L60 #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS) #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.2409.07546

openalex publication_date 2024/09/11 · openalex created_date 2025/01/24 · openalex updated_date 2026/07/30

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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