Phase-Isostable Reduction of Coupled Oscillator Networks #

Robert Allen

10:50 Tuesday in 2Q50/51.

Part of the Neurodynamics session.

Abstract #

For decades, the networks of coupled oscillators that appear all across applied mathematics, including in neuroscience, have been analysed by reducing each oscillator to a single coordinate described by its phase on its limit cycle. However, this requires the assumption that the oscillator is always on cycle, an assumption that breaks down if perturbations are strong or frequent or if relaxation back to cycle is slow. By introducing an ‘Isostable’ coordinate that encapsulates a notion of distance from cycle, the need for this assumption is removed so the phase-isostable reduction better captures the dynamics of the full system. It also allows for the recovery of results that cannot be found using a phase-only description. In this talk, I will describe how we define and derive the phase-isostable reduction of an oscillator, extend this to general coupled networks and show some results about existence and stability of some network states in the phase-isostable framework.