The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability

Abstract

We study the dynamics arising when two identical oscillators are coupled near a Hopfbifurcation where we assume a parameter uncouples the system at = 0. Using anormal form forN= 2 identical systems undergoing Hopf bifurcation, we explore thedynamical properties. Matching the normal form coefficients to a coupledWilson–Cowan oscillator network gives an understanding of different types ofbehaviour that arise in a model of perceptual bistability. Notably, we find bistabilitybetween in-phase and anti-phase solutions that demonstrates the feasibility forsynchronisation to act as the mechanism by which periodic inputs can be segregated(rather than via strong inhibitory coupling, as in the existing models). Using numericalcontinuation we confirm our theoretical analysis for small coupling strength andexplore the bifurcation diagrams for large coupling strength, where the normal formapproximation breaks down.