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arXiv · 1610.00296

Comparing the Locking Threshold for Rings and Chains of Oscillators

Bertrand Ottino-Loffler·Steven Strogatz
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Abstract

We present a case study of how topology can affect synchronization. Specifically, we consider arrays of phase oscillators coupled in a ring or a chain topology. Each ring is perfectly matched to a chain with the same initial conditions and the same random natural frequencies. The only difference is their boundary conditions: periodic for a ring, and open for a chain. For both topologies, stable phase-locked states exist if and only if the spread or "width" of the natural frequencies is smaller than a critical value called the locking threshold (which depends on the boundary conditions and the particular realization of the frequencies). The central question is whether a ring synchronizes more readily than a chain. We show that it usually does, but not always. Rigorous bounds are derived for the ratio between the locking thresholds of a ring and its matched chain, for a variant of the Kuramoto model that also includes a wider family of models.

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Bertrand Ottino-Loffler, Steven Strogatz. 2016-10-02. Comparing the Locking Threshold for Rings and Chains of Oscillators. https://doi.org/10.1103/physreve.94.062203

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