Description nonlinear responses using peak-to-peak values

We put forward a novel method, period sampling peak-to-peak value (PSP) diagram, to describe different types of nonlinear responses in nonlinear dynamical systems. In this method, a two-dimensional graph was plotted. It used the peak-to-peak values as one coordinate and the other was the relevant period sampling numbers. The nonlinear responses of Duffing equation, a retarded nonlinear vehicle suspension system and cracked rotor were studied by this method. The PSP diagrams were composed of dots. The figure for period was a straight line; for multi-period were multi-straight lines; for quasi-period was an orderly period curve; while for chaos, it was out-of-order. Some numerical results are given based on this method and prove its efficiency to distinguish nonlinear responses.