Oscillators with asymmetric single and double well potentials: transition to chaos revisited

We study the Melnikov criterion for a global homoclinic bifurcation and possible transition to chaos for a single degree of freedom nonlinear oscillator. This provides a systematic method of treatment for an arbitrary potential expressed as a fourth order polynomial. The equation of motion has external excitation and a Duffing type nonlinearity with one or two unsymmetric potential wells.