Elimination of chaos in a class of nonlinear oscillators

The system under consideration is a second order nonlinear oscillator subjected to damping force and a periodic disturbance consisting of a sine and a cosine component of the unknown frequency. It is assumed that the potential energy of the oscillator has at least two minimal points. The result proved in this paper is that by proper choice of the damping function chaotic behavior can be eliminated for any value of the unknown frequency In order to apply the result it is necessary to know only the distance between the minimal points of the potential energy and the amplitudes of the sine and the cosine components of the periodic disturbance