The determination of the mechanisms of spiral breakup in excitable media is still an open problem for researchers. In the context\nof cardiac electrophysiological activities, spiral breakup exhibits complex spatiotemporal pattern known as ventricular fibrillation.\nThe latter is the major cause of sudden cardiac deaths all over the world. In this paper, we numerically study the instability of\nperiodic planar traveling wave solution in two dimensions. The emergence of stable spiral pattern is observed in the considered\nmodel. This pattern occurs when the heart is malfunctioning (i.e., ventricular tachycardia).We show that the spiral wave breakup\nis a consequence of the transverse instability of the planar traveling wave solutions.The alternans, that is, the oscillation of pulse\nwidths, is observed in our simulation results. Moreover, we calculate the widths of spiral pulses numerically and observe that the\nstable spiral pattern bifurcates to an oscillatory wave pattern in a one-parameter family of solutions.The spiral breakup occurs far\nbelow the bifurcation when the maximum and the minimum excited states become more distinct, and hence the alternans becomes\nmore pronounced.
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