The transition from periodic to quasiperiodic spiral-wave rotation is studied numerically by the pseudospectral method in a two-variable model of excitable kinetics. Quasiperiodic behavior originates from a supercritical Hopf bifurcation of one branch of circularly rotating spiral-wave solution. The secondary frequency is strongly determined by the presence of a second nearby branch of solution rotating about a larger hole radius. Scaling laws consistent with numerical results are proposed for the spiral-tip orbits in the critical region.
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Alain Karma (1990) studied this question.
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