High-order phase reduction for coupled 2D oscillators

Abstract

Phase reduction is a general approach to describe coupled oscillatory units in terms of their phases, assuming that the amplitudes are enslaved. For such a reduction, the coupling should be small, but one also expects the reduction to be valid for finite coupling. This paper presents a general framework allowing us to obtain coupling terms in higher orders of the coupling parameter for generic two-dimensional oscillators and arbitrary coupling terms. The theory is illustrated with an accurate prediction of Arnold's tongue for the van der Pol oscillator exploiting higher-order phase reduction.

References in corpus (3)

• Phase reduction beyond the first order: the case of the mean-field complex Ginzburg-Landau equation
• Emergent hypernetworks in weakly coupled oscillators
• A parametrisation method for high-order phase reduction in coupled oscillator networks

Cited by in corpus (1)

• Theory of phase reduction from hypergraphs to simplicial complexes: a general route to higher-order Kuramoto models