Replicating spots in reaction-diffusion systems

Kyoung Jin Lee, Harry L. Swinney

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

We review the phenomenon of replicating spots in reaction-diffusion systems and discuss the mechanism of replication. This phenomenon was discovered in recent experiments on a ferrocyanide-iodate-sulfite reaction-diffusion system. Patterns form in a thin gel layer that is in contact with a continuously fed stirred reservoir. Patterns of spots are observed to undergo a continuous process of growth and multiplication through cell division and death through overcrowding. A similar phenomenon is also found in numerical simulations in one dimension on a four-species model of the ferrocyanide-iodate-sulfite reaction and in simulations in two dimensions of simpler two-species reaction-diffusion models: Gray-Scott model by J. Pearson and FitzHugh-Nagumo model by A. Hagberg and E. Meron.

Original languageEnglish
Pages (from-to)1149-1158
Number of pages10
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume7
Issue number5
Publication statusPublished - 1997 May 1
Externally publishedYes

Fingerprint

Reaction-diffusion System
FitzHugh-Nagumo
Reaction-diffusion Model
Cell Division
One Dimension
Replication
Two Dimensions
Multiplication
Model
Contact
Numerical Simulation
Gels
Cells
Experiment
Computer simulation
Simulation
Experiments

ASJC Scopus subject areas

  • General
  • Applied Mathematics

Cite this

Replicating spots in reaction-diffusion systems. / Lee, Kyoung Jin; Swinney, Harry L.

In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 7, No. 5, 01.05.1997, p. 1149-1158.

Research output: Contribution to journalArticle

@article{cbb66ba101a84995a487d1c4d31fe2de,
title = "Replicating spots in reaction-diffusion systems",
abstract = "We review the phenomenon of replicating spots in reaction-diffusion systems and discuss the mechanism of replication. This phenomenon was discovered in recent experiments on a ferrocyanide-iodate-sulfite reaction-diffusion system. Patterns form in a thin gel layer that is in contact with a continuously fed stirred reservoir. Patterns of spots are observed to undergo a continuous process of growth and multiplication through cell division and death through overcrowding. A similar phenomenon is also found in numerical simulations in one dimension on a four-species model of the ferrocyanide-iodate-sulfite reaction and in simulations in two dimensions of simpler two-species reaction-diffusion models: Gray-Scott model by J. Pearson and FitzHugh-Nagumo model by A. Hagberg and E. Meron.",
author = "Lee, {Kyoung Jin} and Swinney, {Harry L.}",
year = "1997",
month = "5",
day = "1",
language = "English",
volume = "7",
pages = "1149--1158",
journal = "International Journal of Bifurcation and Chaos",
issn = "0218-1274",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "5",

}

TY - JOUR

T1 - Replicating spots in reaction-diffusion systems

AU - Lee, Kyoung Jin

AU - Swinney, Harry L.

PY - 1997/5/1

Y1 - 1997/5/1

N2 - We review the phenomenon of replicating spots in reaction-diffusion systems and discuss the mechanism of replication. This phenomenon was discovered in recent experiments on a ferrocyanide-iodate-sulfite reaction-diffusion system. Patterns form in a thin gel layer that is in contact with a continuously fed stirred reservoir. Patterns of spots are observed to undergo a continuous process of growth and multiplication through cell division and death through overcrowding. A similar phenomenon is also found in numerical simulations in one dimension on a four-species model of the ferrocyanide-iodate-sulfite reaction and in simulations in two dimensions of simpler two-species reaction-diffusion models: Gray-Scott model by J. Pearson and FitzHugh-Nagumo model by A. Hagberg and E. Meron.

AB - We review the phenomenon of replicating spots in reaction-diffusion systems and discuss the mechanism of replication. This phenomenon was discovered in recent experiments on a ferrocyanide-iodate-sulfite reaction-diffusion system. Patterns form in a thin gel layer that is in contact with a continuously fed stirred reservoir. Patterns of spots are observed to undergo a continuous process of growth and multiplication through cell division and death through overcrowding. A similar phenomenon is also found in numerical simulations in one dimension on a four-species model of the ferrocyanide-iodate-sulfite reaction and in simulations in two dimensions of simpler two-species reaction-diffusion models: Gray-Scott model by J. Pearson and FitzHugh-Nagumo model by A. Hagberg and E. Meron.

UR - http://www.scopus.com/inward/record.url?scp=0011699805&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0011699805&partnerID=8YFLogxK

M3 - Article

VL - 7

SP - 1149

EP - 1158

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

SN - 0218-1274

IS - 5

ER -