Plasma flow control which based on surface dielectric barrier discharges(DBD)has a rapid development in the past few years.As a active aerodynamic flow control technology,with the significant advantages such as no moving parts,extremely fast response,low mass and power consumption,it is widely considered that it will plays a key role in the future aircraft development and has tremendous potential.At the present time,an increasing amount of research has gone into the study of plasma actuators and also this device have shown its effective in a variety of applications,which included flow separation control,boundary layer attachment,lift increment,drag reduction,combustion efficiency enhancement and noise reduction.As the excitation source of the plasma flow control,the DBD actuator which generates the plasma is the most important device undoubtedly.The performance of the actuator is closely related to the flow control.The specific DBD configuration used for plasma actuators consists of two electrodes,one exposed to the air and the other encapsulated by a dielectric material.Although there are no complicated external structures in the DBD device,however,as a strongly nonlinear internal system,there are still lots of phenomena that have not been explained yet,such as the particles motion and discharge process.So,in this paper,a two-dimensional three particles computational model which includes the electron,positive ions and negative ions is used to predict the complex nonlinear phenomena such as period-doubling and chaos in a dielectric barrier discharge at atmospheric pressure.Furthermore,with the analysis to the complex nonlinear behaviors,it helps to understand the effective mechanisms of the actuator and its effect as an excitation source.Also,the results are meaningful to the parameter choice in plasma flow control.