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We study the dynamics arising when two identical oscillators are coupled neara Hopf bifurcation where we assume a parameter $\epsilon$ uncouples the systemat $\epsilon=0$. Using a normal form for $N=2$ identical systems undergoingHopf bifurcation, we explore the dynamical properties. Matching the normal formcoefficients to a coupled Wilson-Cowan oscillator network gives anunderstanding of different types of behaviour that arise in a model ofperceptual bistability. Notably, we find bistability between in-phase andanti-phase solutions that demonstrates the feasibility for synchronisation toact as the mechanism by which periodic inputs can be segregated (rather thanvia strong inhibitory coupling, as in existing models). Using numericalcontinuation we confirm our theoretical analysis for small coupling strengthand explore the bifurcation diagrams for large coupling strength, where thenormal form approximation breaks down.

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