In this paper, we study the effect of a dichotomous noise on meandering spiral dynamics, and exhibit how the cycloid motion of the meandering spiral tip is destroyed by the noise. Switching on the noise does not alter the primary frequency f_1 and the secondary frequency f_2 in the tip motion, which is different from the case for a periodic dichotomous modulation, where f_2 is changed according to two specific rules. However, the dichotomous noise leads to a decrease of the amplitudes at f_1 and f_2, and the rate of decrease of the amplitude at f_2 is larger than that at f_2 in the process of increasing the noise intensity or the correlation. The areas with small v-values (SV) are defined, and the distribution and size of the SV areas are analyzed, in order to explain and describe these results. It is also proved that spiral waves can be eliminated by the dichotomous noise with a large amplitude or correlation.
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