Numerical phase reduction beyond the first order approximation

2018/11/30 by Michael Rosenblum, Arkady Pikovsky · 1 citation
Physics and Astronomy · #physics.comp-ph #nlin.CD

paper · pdf · doi:10.1063/1.5079617

6 pages, 7 figures

arxiv created 2018/12/05 · arxiv updated 2019/02/20

Abstract

We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for the evolution of the phase. Our simulations demonstrate that the description of the dynamics solely by phase variables can be valid for rather strong coupling strengths and large deviations from the limit cycle. Coupling functions depend crucially on the coupling and are generally non-decomposable in phase response and forcing terms. We also discuss limitations of the approach.

Cited by

• Reconstructing resonant phase oscillator interactions from noisy time series

Related

• Nonlinear phase coupling functions: a numerical study
• High-Order Phase Reduction for Coupled Oscillators
• An Adaptive Phase-Amplitude Reduction Framework Without O(ε) Constraints on Inputs
• Reconstructing phase dynamics of oscillator networks
• Phase reduction approach to synchronization of nonlinear oscillators