CONTROLLING OF CHAOS BY WEAK PERIODIC PERTURBATIONS IN DUFFING-VAN DER POL OSCILLATOR

This paper investigates the possibility of controlling horseshoe and a symptotic chaos in the Duffing-van der Pol oscillator by both periodic parametric perturbation and addition of second periodic force. Using Melnikov method the effect of weak perturbations on horseshoe chaos is studied. Parametric regimes where suppression of horseshoe occurs are predicted. Analytical predictions are demonstrated through direct num erical simulations: Starting from asymptotic chaos we show the recover y of periodic motion for a range of values of amplitude and frequency of the periodic perturbations. Interestingly, suppression of chaos is found in the parametric regimes where the Melnikov function does not c hange sign.