Resonance and chaos behavior in a two-degree-of-freedom Duffing system with cubic coupled terms

The dynamical behaviors for a class of two-degree-of-freedom Duffing system with cubic coupled terms are evaluated, where multiple scale method is adopted to find the first-order steady-state response of the system. The effect of cubic terms on system response is investigated by analyzing the principal resonance and internal resonance, then the bifurcation process is analyzed in terms of the intensity of external force. The numerical results show that besides the route to chaos through period doubling, the system exists a kind of sudden transition route between periodic motion and chaotic vibrations, which are further verified by the top Lyapunov exponent, phase portrait and Poincar mapping analysis on dynamical behavior of the system.