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Knotted reaction-diffusion waves

McDermott, S. and Mulholland, A.J. and Gomatam, J. (2002) Knotted reaction-diffusion waves. Proceedings A: Mathematical, Physical and Engineering Sciences, 458 (2028). pp. 2947-2966. ISSN 1364-5021

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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.