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We carried out a numerical exploration of spiral waves in a typical excitable medium, emphasizing the variety of behaviors encountered while changing two parameters of local excitability: the threshold for starting an excitation and the excitation rate at the wavefront. Within this parameter plane we found domains in which: 1) propagation is impossible, 2) propagation succeeds but there are no spiral waves, 3) spiral waves are stable and strictly periodic, 4) spiral waves exhibit two-period quasiperiodicity, and 5) spiral waves exhibit complex behavior that might be associated with the well-known instability of three-period flows on the three-torus. The boundary curves (bifurcation loci) separating these domains run parallel to the propagation boundary over much of their extent.
Jahnke et al. (Sat,) studied this question.