FOURIER ANALYSIS OF THE COMPLEX MOTION OF SPIRAL TIPS IN EXCITABLE MEDIA

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Abstract
An analysis of spiral tip trajectories by complex Fast Fourier Transform (FFT) is presented. The trajectories are obtained from the numerical integration of partial differential equations describing the Oregonator model of an excitable medium. Their analysis shows: (1) There are regions in the (ε, f) parameter space of the model where for a given ε and increasing f up to four frequency branches appear. The frequencies of these branches determine the coarse structure and geometry of the pattern, i.e., the number and the size of their loops, and are called "structural" frequencies. Other frequencies of the spectra are related with the detailed shape of the loops. (2) The interplay of up to four structural frequencies generates regular trajectories of high complexity but no sign of chaos has been found. (3) The spiral wave outside the core region is independent of the complexity of the tip trajectory. It is solely determined by the structural Fourier component with frequency ν and amplitude r that has the highest circular speed c = 2πrν.

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