The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability
Pérez-Cervera, A; Ashwin, P; Huguet, G; et al.M-Seara, T; Rankin, J
Date: 5 August 2019
Article
Journal
Journal of Mathematical Neuroscience
Publisher
Springer
Publisher DOI
Abstract
We study the dynamics arising when two identical oscillators are coupled near
a Hopf bifurcation where we assume a parameter ε uncouples the system at ε = 0. Using
a normal form for N = 2 identical systems undergoing Hopf bifurcation, we explore the
dynamical properties. Matching the normal form coefficients to a coupled ...
We study the dynamics arising when two identical oscillators are coupled near
a Hopf bifurcation where we assume a parameter ε uncouples the system at ε = 0. Using
a normal form for N = 2 identical systems undergoing Hopf bifurcation, we explore the
dynamical properties. Matching the normal form coefficients to a coupled Wilson-Cowan
oscillator network gives an understanding of different types of behaviour that arise in a
model of perceptual bistability. Notably, we find bistability between in-phase and anti-phase
solutions that demonstrates the feasibility for synchronisation to act as the mechanism by
which periodic inputs can be segregated (rather than via strong inhibitory coupling, as in
existing models). Using numerical continuation we confirm our theoretical analysis for small
coupling strength and explore the bifurcation diagrams for large coupling strength, where
the normal form approximation breaks down.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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