Homoclinic transition to chaos in the Ueda oscillator with external   forcing
  We examine the Melnikov criterion for transition to chaos in case of a single degree of freedom nonlinear oscillator with the Ueda well potential and an external periodic excitation term. Using effective Hamiltonian we have examined homoclinic orbits and cross-sections of stable and unstable manifolds which gave the condition of transition to chaos through a homoclinic bifurcation. 
Grzegorz Litak, Arkadiusz Syta, Marek Borowiec