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arXiv · 2007.14077

High-Order Phase Reduction for Coupled Oscillators

Erik Genge·Erik Teichmann·Michael Rosenblum·Arkady Pikovsky
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Abstract

We explore the phase reduction in networks of coupled oscillators in the higher orders of the coupling parameter. For coupled Stuart-Landau oscillators, where the phase can be introduced explicitly, we develop an analytic perturbation procedure to allow for the obtaining of the higher-order approximation explicitly. We demonstrate this by deriving the second-order phase equations for a network of three Stuart-Landau oscillators. For systems where explicit expressions of the phase are not available, we present a numerical procedure that constructs the phase dynamics equations for a small network of coupled units. We apply this approach to a network of three van der Pol oscillators and reveal components in the coupling with different scaling in the interaction strength.

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Erik Genge, Erik Teichmann, Michael Rosenblum, Arkady Pikovsky. 2020-07-28. High-Order Phase Reduction for Coupled Oscillators. https://arxiv.org/abs/2007.14077

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