bifurcation of a microelectromechanical nonlinear coupling system with delay feedback

Abstract

The dynamics of a kind of electromechanical coupling deformable micromirror device torsion micromirror with delay are investigated. Based on the distribution of eigenvalues, we prove that a sequence of Hopf bifurcation occurs at the equilibrium as the delay increases and obtain the critical values of Hopf bifurcation. Explicit algorithms for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived, using the theories of normal form and center manifold.