Knotted reaction-diffusion waves

S. McDermott; Anthony Mulholland; J. Gomatam

doi:10.1098/rspa.2002.0997

Knotted reaction-diffusion waves

S. McDermott, Anthony Mulholland, J. Gomatam

Research output: Contribution to journal › Article (Academic Journal) › 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
DOIs	https://doi.org/10.1098/rspa.2002.0997
Publication status	Published - 8 Dec 2002

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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.",

author = "S. McDermott and Anthony Mulholland and J. Gomatam",

year = "2002",

month = dec,

day = "8",

doi = "10.1098/rspa.2002.0997",

language = "English",

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

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T1 - Knotted reaction-diffusion waves

AU - McDermott, S.

AU - Mulholland, Anthony

AU - Gomatam, J.

PY - 2002/12/8

Y1 - 2002/12/8

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.

UR - https://pureportal-staging.strath.ac.uk/en/publications/d114ebe7-57ac-4a65-a8d2-b17adb871eb0

U2 - 10.1098/rspa.2002.0997

DO - 10.1098/rspa.2002.0997

M3 - Article (Academic Journal)

SN - 1471-2946

SN - 2053-9150

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

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

ER -

Knotted reaction-diffusion waves

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