Computation of invariant curves in the analysis of periodically forced neural oscillators

Abstract

Background oscillations, reflecting the excitability of neurons, are ubiq- uitous in the brain. Some studies have conjectured that when spikes sent by one population reach the other population in the peaks of excitability, then informa- tion transmission between two oscillating neuronal groups is more effective. In this context, phase locking relationships between oscillating neuronal populations may have implications in neuronal communication as they assure synchronous activity between brain areas. To study this relationship, we consider a population rate model and perturb it with a time-dependent input. We use the stroboscopic map and apply powerful computational methods to compute the invariant objects and their bifur- cations as the perturbation parameters (frequency and amplitude) are varied. The analysis performed shows the relationship between the appearance of synchronous and asynchronous regimes and the invariant objects of the stroboscopic map.