Abstract: Limit cycle flutter and the motion of chaos of two-dimensional airfoil with quadratic nonlinear pitching stiffness in incompressible flow on nonzero equilibrium points are investigated.The center manifold theory is used to reduce a four-dimensional system to a two-dimensional system,and the bifurcation points of the system are determined by bifurcation theory.The type and stability of bifurcation points are determined by computing focal values of system.The type of Hopf bifurcation is determined by the second Lyapunov method of bifurcation problem.The theoretical analysis presented here provides a good agreement with numerical simulations obtained by using a fourth-order Runge-Kutta method.Furthermore, the way leads to chaos in the airfoil system is found and there exits large field of the period-five motion.The results indicate that the bifurcation point is a stable weak focus, when the supercritical Hopf occurs,there exists a stable limit cycle.The motion of chaos occurs due to period-doubling bifurcation.

Key words: nonlinear system, period-doubling bifurcation, limit cycle flutter, center manifold theory, bifurcation point