Abstract: Using the basic concepts of nonlinear science we have studied the cell cycle network dynamics of budding yeast. Our study shows that nonlinear science may play an important role in investigating the dynamic behavior of living organisms quantitatively. Its current limitations are also pointed out, indicating that the application of nonlinear dynamics to the study of living systems not only provides powerful mathematic tools for systems biology, but also promotes the advance of nonlinear science itself. In this respect, our study shows the potential of cross-disciplinary science.