NPG Nonlinear Processes in Geophysics NPG Nonlin. Processes Geophys. 1607-7946 Copernicus Publications Göttingen, Germany 10.5194/npg-21-251-2014 Synchronization of coupled stick-slip oscillators Sugiura N. 1 Hori T. 2 Kawamura Y. 2 Research Institute for Global Change, JAMSTEC, Yokosuka, Japan Institute for Research on Earth Evolution, JAMSTEC, Yokohama, Japan 24 02 2014 21 1 251 267 Copyright: © 2014 N. Sugiura et al. 2014 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://npg.copernicus.org/articles/21/251/2014/npg-21-251-2014.html The full text article is available as a PDF file from https://npg.copernicus.org/articles/21/251/2014/npg-21-251-2014.pdf

A rationale is provided for the emergence of synchronization in a system of coupled oscillators in a stick-slip motion. The single oscillator has a limit cycle in a region of the state space for each parameter set beyond the supercritical Hopf bifurcation. The two-oscillator system that has similar weakly coupled oscillators exhibits synchronization in a parameter range. The synchronization has an anti-phase nature for an identical pair. However, it tends to be more in-phase for a non-identical pair with a rather weak coupling. A system of three identical oscillators (1, 2, and 3) coupled in a line (with two springs <i>k</i><sub>12</sub>=<i>k</i><sub>23</sub>) exhibits synchronization with two of them (1 and 2 or 2 and 3) being nearly in-phase. These collective behaviours are systematically estimated using the phase reduction method.

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