Suppression of chaos by weak resonant excitations in a nonlinear oscillator with a non-symmetric potential

We examine the Mielnikov criterion for transition to chaos in case of one degree of freedom nonlinear oscillator with non symmetric potential. This system subjected to an external periodic force shows homoclinic transition from regular vibrations to chaos just before escape from the potential well. Especially we study the effect of a second resonant excitation with different phase on the system transition to chaos and propose a way of its control.