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Journal Article

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

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Marquardt,  Florian
Marquardt Group, Associated Groups, Max Planck Institute for the Science of Light, Max Planck Society;

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PhysRevE.92.012902.pdf
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Citation

Lauter, R., Brendel, C., Habraken, S. J. M., & Marquardt, F. (2015). Pattern phase diagram for two-dimensional arrays of coupled limit-cycle oscillators. Physical Review E, 92(1): 012902. doi:10.1103/PhysRevE.92.012902.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-63A2-0
Abstract
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.