Bifurcations and chaos in the triple-well Φ6-Van der Pol oscillator driven by external and parametric excitations

The chaotic behavior of a nonlinear damped three-well Φ6-Van der Pol oscillator under external and parametric excitations is studied in detail by means of Melnikovʹs analysis. The predictions are tested against numerical simulations based on the basin of attraction of initial conditions. It is found that the threshold for the onset of chaos in the system increases as the amplitude of the parametric excitation decreases and increases as the amplitude of the external forcing increases. Additionally, the onset of chaos is studied through analysis of the Poincaré map, a construction of the bifurcation diagrams and a computation of the maximal Lyapunov exponent.