Numerical phase reduction beyond the first order approximation

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.

arXiv comment6 pages, 7 figures

References in corpus (1)

• Inference of Time-Evolving Coupled Dynamical Systems in the Presence of Noise

Cited by in corpus (11)

• Networks beyond pairwise interactions: structure and dynamics
• Multiorder Laplacian for synchronization in higher-order networks
• Phase reduction beyond the first order: the case of the mean-field complex Ginzburg-Landau equation
• Fast optimal entrainment of limit-cycle oscillators by strong periodic inputs via phase-amplitude reduction and Floquet theory
• Generalized splay states in phase oscillator networks
• Synchronization transitions in Kuramoto networks with higher-mode interaction
• Phase dynamics of noise-induced coherent oscillations in excitable systems
• High-order phase reduction for coupled 2D oscillators
• Analytical Phase Reduction for Weakly Nonlinear Oscillators
• Phase and amplitude description of complex oscillatory patterns in reaction-diffusion systems
• Comment on "The Winfree model with non-infinitesimal phase-response curve: Ott-Antonsen theory" [Chaos 30, 073139 (2020)]