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

Author
Perez, A.; Ashwin, P.; Huguet, G.; Martinez-seara, M.; Rankin, J.
Type of activity
Journal article
Journal
Journal of Mathematical Neuroscience
Date of publication
2019-12-01
Volume
9
First page
7: 1
Last page
7: 33
DOI
10.1186/s13408-019-0075-2
Repository
http://hdl.handle.net/2117/185418 Open in new window
URL
https://mathematical-neuroscience.springeropen.com/articles/10.1186/s13408-019-0075-2 Open in new window
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 a...
Citation
Perez, A. [et al.]. The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability. "Journal of Mathematical Neuroscience", 1 Desembre 2019, vol. 9, p. 7: 1-7: 33.
Keywords
Bifurcation analysis, Hopf bifurcation, Neural competition, Normal form, Perceptual bistability, Synchrony
Group of research
SD - UPC Dynamical Systems

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