An alternative approach to Poincare sectioning in weakly nonlinear systems

A large array of dynamical systems can be broadly classified as weakly nonl inear, where a common feature is the presence of dual time-scale dynamics. Often it is desirable to isolate the dynamics at one time scale (typically the slower time scale), and this paper presents a generic phase-sensitive d etection method that successfully isolates the slow-time dynamics, strippin g off the less-relevant and often dominant fast-time dynamics. We shall als o show for the first time, under certain phase considerations, the equivale nce of the present method and the traditional Poincare section of the origi nal full response. The method is first presented in theory and then applied to data from a numerical simulation of the forced spherical pendulum follo wed by data from a similar spherical pendulum experiment. The method is suc cessful provided certain conditions apply for phase stationarity.