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.
|Journal||Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences|
|Publication status||Published - 1 Dec 2002|
- stationary solutions
- eikonal equation