Suppression of chaos in averaged oscillator driven by external and parametric excitations

Controlling chaos in a nonlinear oscillator subjected to external and parametric excitations having incommensurate frequencies is discussed. An averaging method is first applied to reduce the original quasi-periodically driven system to a periodically driven one. The Melnikov method is applied on the reduced periodically driven system and the Melnikov function is subsequently established. The possibility of achieving a suitable system for the control of chaos in the averaged system by introducing a third harmonic parametric component into the cubic term of the original one is investigated.