Knotted reaction-diffusion waves

S. McDermott; A.J. Mulholland; J. Gomatam

doi:10.1098/rspa.2002.0997

Knotted reaction-diffusion waves

S. McDermott, A.J. Mulholland, J. Gomatam

Mathematics And Statistics

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
Pages (from-to)	2947-2966
Number of pages	19
Journal	Proceedings A: Mathematical, Physical and Engineering Sciences
Volume	458
Issue number	2028
DOIs	https://doi.org/10.1098/rspa.2002.0997
Publication status	Published - 8 Dec 2002

Keywords

Reaction-Diffusion Knots Eikonal Equation Stationary Solutions

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10.1098/rspa.2002.0997

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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.",

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AU - Gomatam, J.

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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 Knots Eikonal Equation Stationary Solutions

UR - http://dx.doi.org/10.1098/rspa.2002.0997

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DO - 10.1098/rspa.2002.0997

M3 - Article

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EP - 2966

JO - Proceedings A: Mathematical, Physical and Engineering Sciences

JF - Proceedings A: Mathematical, Physical and Engineering Sciences

IS - 2028

ER -

Knotted reaction-diffusion waves

Abstract

Keywords

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