When spiral waves are present in a 2-dimensional model of excitable media, we find that the state of each cell stays reasonably close to a one-dimensional manifold. Using isostable reduction and Hamilton-Jacobi-Bellman techniques, we develop a novel energy-optimal methodology to synchronize the activity of the cells. This methodology has potential applications to cardiac arrhythmia. Specifically, it represents a significant first step in the development of energy-optimal defibrillation strategies.
Animation and figures are taken from:
D. Wilson, and J. Moehlis. "An Energy-Optimal Methodology for Synchronization of Excitable Media." SIAM Journal on Applied Dynamical Systems 13.2 (2014): 944-957.