PMID: 11328154May 1, 2001Paper

Phase diagram for the Winfree model of coupled nonlinear oscillators

Physical Review Letters
J T Ariaratnam, S H Strogatz

Abstract

In 1967 Winfree proposed a mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators. Here we give the first bifurcation analysis of the model, for a tractable special case. The system displays rich collective dynamics as a function of the coupling strength and the spread of natural frequencies. Besides incoherence, frequency locking, and oscillator death, there exist hybrid solutions that combine two or more of these states. We present the phase diagram and derive several of the stability boundaries analytically.

References

Sep 1, 1988·The Quarterly Review of Biology·J Buck
Mar 1, 1971·Journal of Neurophysiology·P S Stein
Jul 1, 1967·Journal of Theoretical Biology·A T Winfree
Dec 1, 1994·Journal of Computational Neuroscience·C Van VreeswijkG B Ermentrout
Nov 15, 1996·Neural Computation·W GerstnerJ D Cowan
Oct 21, 2000·Physical Review Letters·G KozyreffP Mandel

❮ Previous
Next ❯

Citations

Apr 25, 2012·Journal of Mathematical Biology·Paola Malerba, Nancy Kopell
Mar 7, 2006·Journal of Computational Neuroscience·Bard Ermentrout, David Saunders
Jan 6, 2011·Journal of Computational Neuroscience·G Bard ErmentroutTheoden I Netoff
Sep 5, 2002·Medical Hypotheses·G T Matioli
May 25, 2007·Neural Computation·Daniele MarinazzoStan C A M Gielen
Nov 15, 2006·The Journal of Chemical Physics·Ya Ping Li, Wei Liang Cao
Jan 8, 2016·Journal of Mathematical Neuroscience·Peter AshwinRachel Nicks
Oct 3, 2015·Chaos·Arkady Pikovsky, Michael Rosenblum
Dec 31, 2003·Developmental Biology·Padmashree C G RidaYun Jin Jiang
Dec 9, 2014·PloS One·Zahra Ghasemi Esfahani, Alireza Valizadeh
Feb 3, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M A ZaksL Schimansky-Geier
Jul 13, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·L AngeliniS Stramaglia
Sep 28, 2004·Physical Review Letters·Yu MaistrenkoP A Tass
Feb 7, 2018·Journal of Mathematical Neuroscience·Carlo R Laing
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Oleksandr V PopovychPeter A Tass
Dec 31, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jan Eric Sträng, Per Ostborn
May 23, 2006·Physical Review Letters·Sung Joon MoonI G Kevrekidis
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·D Dane QuinnSteven H Strogatz
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·F GiannuzziS Stramaglia
Sep 15, 2016·Physical Review. E·Amitava Banerjee, Muktish Acharyya
Dec 14, 2011·Bioinspiration & Biomimetics·Takuro Moriyama, Daisuke Kurabayashi
May 29, 2020·Journal of Mathematical Neuroscience·Christian BickErik A Martens
Dec 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Carlo R Laing
Jun 30, 2018·Physical Review Letters·Ernest Montbrió, Diego Pazó
Mar 24, 2020·Nature Materials·Midya PartoMercedeh Khajavikhan
Jan 20, 2018·Physical Review. E·Rafael GallegoDiego Pazó
Feb 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yasuaki Kobayashi, Hiroshi Kori
Feb 12, 2021·Journal of Mathematical Biology·Yujie Ding, Bard Ermentrout
Mar 2, 2021·Frontiers in Systems Neuroscience·Carlo R LaingShawn Means
Oct 4, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Slaven Peles, Kurt Wiesenfeld
Jun 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Per Ostborn
Dec 31, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E OhB Kahng
Apr 20, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Qian Shu Li, Ya Ping Li

❮ Previous
Next ❯

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.

Related Papers

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Paulo F C TillesHilda A Cerdeira
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Yu-Feng LuBing-Hong Wang
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Takashi Ichinomiya
© 2021 Meta ULC. All rights reserved