Nonlinear dynamics of pulsating instability in radiating counterflow diffusion flames is numerically investigated by imposing Damk$ddot{o}$hler number perturbation. Stable limit-cycle solutions occur in small ranges of Damk$ddot{o}$hler numbers past bifurcation point of instability. Period doubling cascade and chaotic behaviors appear just before dynamic extinction occurs. Nonlinear dynamics is also studied when large disturbances are imposed to flames. For weak steady flames, the dynamic extinction range shrinks as the magnitudes of disturbances are increased. However, strong steady flames can overcome relatively large disturbances, thereby the dynamic extinction range extending. Stable limit-cycle behaviors reappears prior to dynamic extinction when the steady flames are strong enough.