Chaos in the triple-well Φ6-van der Pol oscillator driven by periodically external and nonlinear parametric excitations

The chaotic dynamics of a nonlinear damped triple-well Phi(6)-van der Pol oscillator under periodically external and nonlinear parametric excitations is studied. Chaos arising from homoclinic and heteroclinic crossings is analyzed using Melnikov method. The chaotic behaviors are compared with a periodically external excitation, a linear parametric excitation and a nonlinear parametric excitation. The critical curves which separate the chaotic regions from the non-chaotic regions are plotted. Especially, there is "a controllable frequency" leading to no chaos for all excitation amplitudes.