Tracking symmetry-breaking in a model for hearing with delay #

Asim Alawfi, Jan Sieber, James Rankin

15:50 Monday in 4Q07.

Part of the Neurons and networks session.

Abstract #

Ferrario and Rankin (2021) introduced a model for auditory (hearing) perception, which couples two identical neural populations of excitatory and inhibitory neurons. The cross-inhibition coupling has a delay such that the model is a four-dimensional system of periodically forced delay differential equations with reflection symmetry. The symmetry breaking coincides with the switching between different auditory perceptions. Bifurcation analysis for this model finds the precise boundaries between the different regimes discussed by Ferrario and Rankin (2021) and predicts a further phenomenon, which may guide future experiments. An essential tool for our bifurcation analysis are extended systems for tracking symmetry-breaking bifurcations of periodic solutions in delay differential equations, newly implemented in DDE-Biftool.