Frequency coupling model for dynamics of responses to stimuli in plasmodium of Physarum polycephalum

Gathering or escaping behavior in the plasmodium of Physarum polycephalum is considered to relate to an entrainment of the coupled nonlinear oscillators. The behavior has been explained to be caused by the formation of phase gradient between those oscillators, which results from the local frequency modulation at the stimulated site. However, it has not yet been elucidated how the formation process relates to the migration of the plasmodium. In this paper, we have introduced a model with frequency coupling besides the phase coupling in the system of coupled oscillators. By the simulation, we have shown that not only the phase gradient but also the concentration gradient of substances such as Ca2+ and ATP are self-organized and their reverse by the stimulus results in the migration of plasmodium.