Suppression of chaos by selective resonant parametric perturbations

It is shown that, depending on its amplitude, frequency, and initial phase, a time-dependent periodic parametric perturbation can suppress chaos in nonlinear oscillators. The example of the Duffing-Holmes oscillator is used to demonstrate that all the numerically and experimentally observed phenomenology is theoretically explained by using the Melnikov-Holmes method and suppression of chaos is seen to be possible when certain resonant frequencies are involved.