The complex dynamic behavior of the mechanical centrifugal flywheel governor system was studied.The dynamical equation of the sysablished using lagrangian and Newton's second law,The chaotic behavior of the system was analyzed by means of bifurcation diagram and Lyapunov exponents.The evolution from Hopf bifurcation to chaos was shown by the shown by the bifurcation diagrams and a series of Poincaré sections under different sets of system parameters,and the bifurcation diagrams were verified by the related Lyapunov exponent spectra.Based on Lyapunov stability theory theory,a method of non-linear control was proposed for synahronization between Duffing system and mechanical centrifugal flywheel govvernor system was realized by aonstructing the appropriate non-linear controller.Numerical simulation shows the effectiveness and feassibility of the proposed method.