Bifurcations of a micro-electromechanical nonlinear coupling system

The dynamical behavior of a micro-electromechanical nonlinear coupling system - deformable micromirror device, is investigated in this paper. In the literature some nonlinear phenomena have been explored by using the numerical method, and saddle-node bifurcation and periodic motions were discovered numerically. Overcoming the obstacle of the unsolvable of the equilibrium points, we analytically obtain the number and stability of the equilibrium points of the system discussed. The saddle-node bifurcation is obtained through the analytic method. Further, both codimension two bifurcations are revealed by the rigorous analysis. Finally, numerical simulations are in good agreement with the theoretical analysis.