ArticleJournal of mathematical neuroscience2019
The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability.
Article in Journal of mathematical neuroscience, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- A framework for macroscopic phase-resetting curves for generalised spiking neural networks.PLoS computational biology · 2022Article
- Phase-locking patterns underlying effective communication in exact firing rate models of neural networks.PLoS computational biology · 2022Article
- Auditory streaming emerges from fast excitation and slow delayed inhibition.Journal of mathematical neuroscience · 2021Article
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5 authors.
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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 [Formula: see text]. Using a normal form for [Formula: see text] 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 the 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.
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