Oscillations and chaos in driven quasi-periodic oscillators

In this paper we study the dynamics of a weakly nonlinear single-degree-of-freedom system subjected to parametric and external excitations. An asymptotic method is used to analyze the bifurcations of quasi-periodic solutions near strong resonances. By applying the Melnikov technique to the reduced system, it is shown that there exists transversal homoclinic orbits resulting in chaotic dynamics. By introducing a nonlinear resonant parametric perturbation in the system we analyze how chaos can be suppressed.