The typical airfoil section system with freeplay described by a piecewise-stiffness model was studied. The pitch angle at the maximum amplitude was chosen as the quasi-Poincaré sections to obtain numerically the bifurcation diagram with change of flight speed. It was found the trans-critical flutter area was located on flight speed of Ma=0.71-0.75 and limit cycle oscillation area located on flight speed of Ma=0.75-0.95 based on the bifurcation diagram. The stability of limit cycle oscillation was analyzed through the constructed four-dimensional map. According to the stability and motion manifold theory

it was learnt that the attraction basin of the limit cycle oscillation was located in the interior region of limit cycle

which was validated by the numerical method at last. At the same time

the coexistence of multiple solutions and various forms of bifurcation phenomena were found in trans-critical flutter area

such as the direct transition from double periodic motion to chaos

the coexistence of multiple periodic motion and double periodic motion

and the phenomenon of jump on amplitude.