In this paper, a response integral quantity method is proposed. This technique provides a quantitative characterization of system responses and can assist the role of the traditional stroboscopic technique (Poincaré section method) in observing bifurcations and chaos of the nonlinear oscillators. We numerically analyze and identify the chaos and subharmonic responses in the forced coupled Duffing's oscillators in which we find that chaotic behaviors and high-order subharmonic responses exist. Due to the signal response contamination of system, it is difficult to identify the high-order responses of the subharmonic motion because of the sampling points on Poincaré map being very close to each other. Even the system responses are subject to misjudgments. The simulation results, however, show that the highorder subharmonic and chaotic responses and their bifurcations can be observed effectively.
