Global Bifurcations in a Class of Two-Degree-ofª²Freedom Systems with Quadratic and Cubic Nonlinearity and 1:2 Internal Resonance
Liang Jianshu, Chen Yushu
(School of Mechanical Engineering, Tianjin University, 300072)

Abstract: In this paper, global bifurcations in a class of nonlinear dynamical systems is investigated. Firstly, using the method of multiple scales, the amplitude and phase modulation equations are determined. Secondly, a near-integrable two-degree-of-freedom system is obtained by a series of transformations. Employing the energy-phase criterion, the condition of existence of Silnikov orbits is determined under Hamiltonian resonance. The condition is confirmed by numerical simulations.
Keywords: Melnikov theory, the energy-phase criterion, Silnikov orbit, Global bifurcation.