Analytical Phase Reduction for Weakly Nonlinear Oscillators

Abstract

Phase reduction is a dimensionality reduction scheme to describe the dynamics of nonlinear oscillators with a single phase variable. While it is crucial in synchronization analysis of coupled oscillators, analytical results are limited to few systems. In this letter, we analytically perform phase reduction for a wide class of oscillators by extending the Poincaré-Lindstedt perturbation theory. We exemplify the utility of our approach by analyzing an ensemble of Van der Pol oscillators, where the derived phase model provides analytical predictions of their collective synchronization dynamics

arXiv comment10 pages, 5 figures

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Cited by in corpus (4)

• Theory of phase reduction from hypergraphs to simplicial complexes: a general route to higher-order Kuramoto models
• Pinning control of chimera states in systems with higher-order interactions
• Gaussian Process Phase Interpolation for estimating the asymptotic phase of a limit cycle oscillator from time series data
• Optimal interaction functions realizing higher-order Kuramoto dynamics with arbitrary limit-cycle oscillators