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

Controlling chaos in a nonlinear oscillator subjected to external and param etric excitations having incommensurate frequencies is discussed. An averag ing method is first applied to reduce the original quasi-periodically drive n system to a periodically driven one. The Melnikov method is applied on th e reduced periodically driven system and the Melnikov function is subsequen tly established. The possibility of achieving a suitable system for the con trol of chaos in the averaged system by introducing a third harmonic parame tric component into the cubic term of the original one is investigated. (C) 2000 Elsevier Science Ltd. All rights reserved.