Cooperative relationships exist among various physical phenomena. Several cooperative phenomena have been analyzed theoretically by considering them as synchronous phenomena. We focus on the cooperative motion obtained in the antagonistic structures by considering the McKibben pneumatic actuator (MPA) as one of the synchronous phenomena. This study aims to realize the various movements of a robot with MPAs based on the autonomous coordination between MPAs. In a previous study, we proposed a novel tension feedback control inspired by animal motion and confirmed that this control law generates some cooperative relationship between the MPAs. In this paper, we mathematically analyze the realized cooperative relationships as a synchronous phenomenon, and clarify the mechanism by which the delay in the change in the MPA length with the change in the MPA pressure generates the transition of phase difference. This result suggests that multiple targeted motions can be generated by a single control law.