Knotted reaction–diffusion waves

Sean McDermott; Anthony J. Mullholland; Jagannathan Gomatam

Knotted reaction–diffusion waves

Sean McDermott, Anthony J. Mullholland, Jagannathan Gomatam

Glasgow Caledonian University

Research output: Contribution to journal › Article › peer-review

Abstract

The prevalence of toroidal scroll waves in experimental studies of excitable reaction– diffusion media motivates this study. To understand the dynamics of these structures in three dimensions we study their interactions with a toroidal manifold. Using an eikonal formulation we demonstrate the existence and stability of both rigidly rotating knotted-waveforms and stationary solutions. We also show that the full reaction– diffusion system supports knotted waves, with good quantitative agreement with the eikonal formulation.

Original language	English
Journal	Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences
Publication status	Published - 1 Dec 2002

Keywords

reaction–diffusion
stationary solutions
knots
eikonal equation

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title = "Knotted reaction–diffusion waves",

abstract = "The prevalence of toroidal scroll waves in experimental studies of excitable reaction– diffusion media motivates this study. To understand the dynamics of these structures in three dimensions we study their interactions with a toroidal manifold. Using an eikonal formulation we demonstrate the existence and stability of both rigidly rotating knotted-waveforms and stationary solutions. We also show that the full reaction– diffusion system supports knotted waves, with good quantitative agreement with the eikonal formulation.",

keywords = "reaction–diffusion, stationary solutions, knots, eikonal equation",

author = "Sean McDermott and Mullholland, {Anthony J.} and Jagannathan Gomatam",

note = "Originally published in: Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences (2002), 458 (2028), pp.2947-2966.",

year = "2002",

month = dec,

day = "1",

language = "English",

journal = "Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences",

issn = "1364-5021",

publisher = "The Royal Society",

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T1 - Knotted reaction–diffusion waves

AU - McDermott, Sean

AU - Mullholland, Anthony J.

AU - Gomatam, Jagannathan

N1 - Originally published in: Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences (2002), 458 (2028), pp.2947-2966.

PY - 2002/12/1

Y1 - 2002/12/1

N2 - The prevalence of toroidal scroll waves in experimental studies of excitable reaction– diffusion media motivates this study. To understand the dynamics of these structures in three dimensions we study their interactions with a toroidal manifold. Using an eikonal formulation we demonstrate the existence and stability of both rigidly rotating knotted-waveforms and stationary solutions. We also show that the full reaction– diffusion system supports knotted waves, with good quantitative agreement with the eikonal formulation.

AB - The prevalence of toroidal scroll waves in experimental studies of excitable reaction– diffusion media motivates this study. To understand the dynamics of these structures in three dimensions we study their interactions with a toroidal manifold. Using an eikonal formulation we demonstrate the existence and stability of both rigidly rotating knotted-waveforms and stationary solutions. We also show that the full reaction– diffusion system supports knotted waves, with good quantitative agreement with the eikonal formulation.

KW - reaction–diffusion

KW - stationary solutions

KW - knots

KW - eikonal equation

M3 - Article

JO - Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences

JF - Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences

SN - 1364-5021

ER -