Analysis methods of phase propagation in autonomic oscillation of Physarum polycephalum

A method for analysing the phase propagation in autonomic oscillation of Physarum polycephalum is described. Physarum polycephalum is often used for the study of autonomous distributed systems of natural organisms. When it moves coordinatively approaching to or from from the local stimulation, the propagation of the phase wave is observed in the surface. By analyzing spatial and temporal propagation of phase wave, we can find the rules of interaction between the oscillators. In this paper, which is about the analysis methods for the propagation of phase, the contour pattern of the analysis almost corresponds to that of the fundamental harmonic frequency series. Also, it is confirmed that Physarum polycephalum has the characteristic of a non-local connection. Phase propagation for repellent stimulation shows a discontinuity of phase which is not observed for attractant stimulation by using mutual information analysis