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.
|Number of pages||19|
|Journal||Proceedings A: Mathematical, Physical and Engineering Sciences|
|Publication status||Published - 8 Dec 2002|
- Reaction-Diffusion Knots Eikonal Equation Stationary Solutions
McDermott, S., Mulholland, A. J., & Gomatam, J. (2002). Knotted reaction-diffusion waves. Proceedings A: Mathematical, Physical and Engineering Sciences, 458(2028), 2947-2966. https://doi.org/10.1098/rspa.2002.0997