Abstract: With the theory of iterative mapping and stabilityanalysis, the harmonic excitation response and periodic response stabilityof a vertical impact damper system is studied. First, the equation ofparameter boundary of stable response is set up. General rules oftransformation from stability to chaos are analyzed. Finally, numericalresults with a better damper effect are obtained by analyzing a typicalquadratic periodic response vibration system. The vibration reduction effectsfor stable state periodic response around the region are discussed.