Entrainment of two coupled van der Pol oscillators by an external oscillation. As a base of "holonic control"

A system composed of two coupled internal oscillators and an external oscillation is studied as a model of biological control systems. The type of interaction between the internal oscillators is a mutual and dissipative one. Three macroscopic states of the internal oscillators are demonstrated in the absence of the external oscillation. Strict and loose entrainment regions of the internal oscillators by the external oscillation are shown in respect to the intensity of the mutual interaction, the intrinsic frequency difference of the internal oscillations, and the magnitude and frequency of the external oscillation. On the other hand, an idea of "holonic system" is introduced and the fundamental properties of the model as a holonic system are elucidated.