Knotted reaction–diffusion waves

Sean McDermott, Anthony J. Mullholland, Jagannathan Gomatam

Research output: Contribution to journalArticlepeer-review


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.


  • reaction–diffusion
  • stationary solutions
  • knots
  • eikonal equation


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