Rachel Nicks (University of Nottingham) – Oscillatory neural dynamics in a phase-amplitude framework

Oscillatory neural dynamics in a phase-amplitude framework

Model reduction techniques can provide useful insight into the dynamics behaviour of high dimensional oscillatory systems such as networks of neurons or neural field models. In this talk we will discuss the recently introduced phase-isostable framework which extends the classical technique of phase reduction to include a notion of a distance from limit cycle. This allows for representation of off cycle trajectories, the description of a greater variety of dynamics and greater accuracy in capturing the behaviour of the full model. We will highlight how this framework can be utilised to reveal bifurcations of phase-locked states in discrete networks and how this can be extended to networks with conduction delays and networks where the node oscillations are induced by delays. If time allows, we will also see how the framework can be applied to continuum neural field models to investigate instabilities of oscillatory phase waves to more exotic patterned states.

[1] R Nicks, R Allen and S Coombes 2024 Insights into oscillator network dynamics using a phase-isostable framework, Chaos, Vol 34, 013141

[2]  R Nicks, R Allen and S Coombes 2024 Phase and amplitude responses for delay equations using harmonic balance, Physical Review E, Vol 110, L012202