Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation

Abstract

The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to DuffingVan der Pol strong nonlinearity by introducing the undetermined fundamental frequency. Then the bifurcation values of homoclinic structure formation are detected through the combined application of the new averaged equations with Melnikov integration. Finally, the explicit application shows the analytical conditions coincide with the results of numerical simulation even disturbing parameter is of arbitrary magnitude. global bifurcation, strongly nonlinear, chaos, Melnikov method Citation:Wang W, Zhang Q C, Feng J J. Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation.

Chaotic threshold for a class of impulsive differential system

“…Furthermore, as can be seen in Figs. 6e and 7c, the structure of the attractor differs significantly from the one obtained in the smooth system [27][28][29].…”