An integration method for detecting chaotic responses of nonlinear systems subjected to double excitations

A methodology designed for identifying chaos of the nonlinear systems subjected to double excitations is proposed. Based on simulations in this study, it is shown by bifurcation diagram that method of Poincaré sections, the conventional chaos-observing method, fails to pinpoint the onset of chaotic motions with the nonlinear systems subjected to double excitations. To remedy this problem, “K_s integration method” is proposed, which integrates the distance between trajectories and origin in phase plane over an excitation period and designates the obtained integration values as K_s's to take the roles of the sampling points derived by Poincaré sections in constructing bifurcation diagram. This “K_s integration method” is shown capable of providing valuable information in bifurcation diagram such that the parameter range leading to chaos can be easily decided and the number of distinguishable time-domain responses can be determined.