Transition to Chaos in the Self-Excited System with a Cubic Double Well   Potential and Parametric Forcing
  We examine the Melnikov criterion for a global homoclinic bifurcation and a possible transition to chaos in case of a single degree of freedom nonlinear oscillator with a symmetric double well nonlinear potential. The system was subjected simultaneously to parametric periodic forcing and self excitation via negative damping term. Detailed numerical studies confirm the analytical predictions and show that transitions from regular to chaotic types of motion are often associated with increasing the energy of an oscillator and its escape from a single well. 
Grzegorz Litak, Marek Borowiec, Arkadiusz Syta, Kazimierz Szabelski