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oai:recercat.cat:2117/1854182026-01-14T07:29:44Zcom_2072_1033col_2072_452950

The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability Pérez Cervera, Alberto Ashwin, Peter Huguet Casades, Gemma Rankin, James Martínez-Seara Alonso, M. Teresa Àrees temàtiques de la UPC::Matemàtiques i estadística Synchrony Perceptual bistability Bifurcation analysis Normal form Neural competition Hopf bifurcation Classificació AMS::65 Numerical analysis 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. Peer Reviewed Postprint (published version) 2019-12-01 Article https://mathematical-neuroscience.springeropen.com/articles/10.1186/s13408-019-0075-2 http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Open Access Attribution-NonCommercial-NoDerivs 3.0 Spain