Hopf Bifurcation Analysis for a Mechanical Centrifugal Flywheel Governor System

The complex dynamic behavior of the mechanical centrifugal flywheel governor system is studied. The dynamical equation of the system is established using Lagrangian and Newtonpsilas second law. The bifurcation behavior and stability of the mechanical centrifugal flywheel governor system is studied. The critical value of Hopf bifurcation is calculated, and the stability of the limit cycle is also discussed. The bifurcation diagram of the system is obtained by the fourth order Runge-Kutta method. The characteristics of the system responses are analyzed by means of Poincare sections and the Lyapunov exponents. Numerical simulation results show that Hopf bifurcation exists in the bifurcation diagram of the system. The evolution from Hopf bifurcation to chaos is shown by the bifurcation diagrams and a series of Poincare sections under different sets of system parameters, and the bifurcation diagrams are verified by the related Lyapunov exponent spectra.