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

Journal of Mathematical Neuroscience
Alberto Pérez-CerveraJames Rankin

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.

References

Jan 1, 1989·Psychological Review·R Blake
Jan 1, 1985·Vision Research·S AnstisA I Cogan
Jan 1, 1972·Biophysical Journal·H R Wilson, J D Cowan
Jul 8, 1980·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·S M Anstis
Aug 11, 1983·Nature·V S Ramachandran, S M Anstis
Nov 1, 1995·Bulletin of Mathematical Biology·G N BorisyukD Roose
Nov 14, 1997·Proceedings of the National Academy of Sciences of the United States of America·P FriesW Singer
Apr 5, 2002·Journal of Computational Neuroscience·Carlo R Laing, Carson C Chow
Feb 22, 2003·Vision Research·Jean-Michel Hupé, Nava Rubin
Apr 1, 1953·Journal of Experimental Psychology·H WALLACH, D N O'CONNELL
Oct 1, 1964·Scientific American·P A KOLERS
Nov 13, 2003·Proceedings of the National Academy of Sciences of the United States of America·Hugh R Wilson
May 20, 2004·Vision Research·Lee A Gilroy, Howard S Hock
Sep 27, 2005·Vision Research·Yee-Joon KimSatoru Suzuki
Jul 11, 2006·Current Biology : CB·Daniel Pressnitzer, Jean-Michel Hupé
Nov 13, 2008·Cognitive Neurodynamics·Deliang Wang, Peter Chang
Jan 7, 2009·Journal of Computational Neuroscience·Asya ShpiroJohn Rinzel
Jul 22, 2011·Journal of Neurophysiology·Jeffrey Seely, Carson C Chow
Jul 13, 2013·Frontiers in Computational Neuroscience·Zachary P Kilpatrick
Nov 13, 2015·PLoS Computational Biology·James RankinJohn Rinzel
Dec 5, 2015·Frontiers in Systems Neuroscience·Edward W LargeMarc J Velasco
Jan 7, 2016·Frontiers in Computational Neuroscience·Ji Chul Kim, Edward W Large
Jan 8, 2016·Journal of Mathematical Neuroscience·Peter AshwinRachel Nicks
May 4, 2016·PLoS Computational Biology·Shashaank VattikutiCarson C Chow
Dec 10, 2016·Journal of Vision·Andrew Isaac MesoGuillaume S Masson
Feb 16, 2017·Annals of the New York Academy of Sciences·Joel S Snyder, Mounya Elhilali
Jul 12, 2017·Proceedings of the National Academy of Sciences of the United States of America·Hsin-Hung LiDavid J Heeger

❮ Previous
Next ❯

Citations

May 4, 2021·Journal of Mathematical Neuroscience·Andrea Ferrario, James Rankin

❮ Previous
Next ❯

Software Mentioned

biggl

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.