Human-robot physical interaction is an important subject for housekeeping, elderly care and entertainment robots. To make a natural physical interaction the entrainment between human and robot motions accomplishes an important role. From this view point we proposed to use neural oscillators for human-robot handshaking [2]. We can make synchronized rhythmic motions in human-robot interaction by the proposed method, since a neural oscillator has a function of synchronization and entrainment with the input signal. However there is a drawback of the method. It is no simple matter to find appropriate values of parameters of the neural oscillator. There are many parameters to be determined, and the effects of the parameters to the characteristics of the neural oscillator are related each other. In this paper we propose a design method of dynamics to generate synchronization and entrainment in human-robot interaction instead of the neural oscillators. We utilize a polynomial design of the nonlinear dynamics and extend the method to synchronization based control of human-robot interaction. The validity of the design method is examined by the simulation of mutual interaction between two vector fields.