Suppression of chaos by resonant parametric perturbations

Starting from a chaotic regime in the dynamics of a Duffing-Holmes oscillator, we show how it is possible, by means of a small parametric perturbation of suitable frequency, to bring the system to a regular regime. This situation is studied from the analytic point of view using the Melnikov method and from the numerical point of view computing Lyapunov exponents. The corresponding bounds for the perturbation are compared. Noting that the time, measured along the original unperturbed separatrix, that elapses between two successive homoclinic intersections grows when we approach the resonance, we propose a possible scenario for this type of regularization of the dynamics.