N. F. Otani and R. Hwa, Topological Considerations in the Generation of Scroll Waves in Excitable and Cyclical Media, Physica D 77 434-455 (1994).
An attempt is made to understand in what manner, and to what extent, the notion of phase, useful in extended media exhibiting cyclical local dynamics, is applicable to the behavior of waves propagating in excitable media. Computer simulations of two situations are examined in each of the two types of media, and the results analyzed. One of these two situations involves a new scroll wave generation mechanism which produces two scroll waves rotating in the same direction. For the simulations conducted for this study, topological arguments involving the phase are relevant for exctable media, but applicaion of the arguments requires careful consideration of the details of the dynamics. Several examples of these principles, as observed in the simulations, are described. One of these examples also leads to an additional observation--that crossing scroll wave filaments probably can not "reconnect" to form essentially parallel filaments in the case of FizHugh-Nagumo dynamics.