Bifurcation Control of Mechanical System with Periodic Coefficients

In order to control the bifurcation behavior at the equilibrium point of the differential system with periodic coefficients losing its stability, the methods for bifurcation control for the dynamical system with constant coefficients, such as using the linear controller, parameter method, and translation, were applied to a mechanical system with periodic coefficients by the Floquet-Lyapunov theory. Then, the related controllers were designed, and its validity in controlling the bifurcation behavior at the equilibrium point was tested through numerical calculation. The results show that translation is invalid to control the Flip and Hopf bifurcations at the equilibrium point in mechanical system with periodic coefficients. When a 2-periodic point is generated by the period-doubling Flip bifurcation at the unstable equilibrium point, either of the linear controller and the parameter method can be used to control the 2-periodic point back to a 1-periodic point. When a Hopf circle is generated by Hopf bifurcation after the equilibrium point loses its stability, the linear controller and the parameter method are all effective for controlling the Hopf circle to a 1-periodic point.