Pattern phase diagram for two-dimensional arrays of coupled limit-cycle oscillators

Arrays of coupled limit-cycle oscillators represent a paradigmatic example for studying synchronization and pattern formation. We find that the full dynamical equations for the phase dynamics of a limit-cycle oscillator array go beyond previously studied Kuramoto-type equations. We analyze the evolu...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2015-07, Vol.92 (1), p.012902-012902, Article 012902
Main Authors: Lauter, Roland, Brendel, Christian, Habraken, Steven J M, Marquardt, Florian
Format: Article
Language:English
Subjects:
Models, Theoretical
Motion
Periodicity
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Summary:Arrays of coupled limit-cycle oscillators represent a paradigmatic example for studying synchronization and pattern formation. We find that the full dynamical equations for the phase dynamics of a limit-cycle oscillator array go beyond previously studied Kuramoto-type equations. We analyze the evolution of the phase field in a two-dimensional array and obtain a "phase diagram" for the resulting stationary and nonstationary patterns. Our results are of direct relevance in the context of currently emerging experiments on nano- and optomechanical oscillator arrays, as well as for any array of coupled limit-cycle oscillators that have undergone a Hopf bifurcation. The possible observation in optomechanical arrays is discussed briefly.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.92.012902