Suppression of chaos by nonresonant parametric perturbations

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Abstract
It is shown analytically and numerically that the suppression of chaos may be effectively achieved by applying a high-frequency parametric force to a chaotic dynamical system. Such a periodic nonresonant force may decrease or even completely eliminate chaos. Taking the Duffing oscillator as a concrete but rather general example, an analytical approach is elaborated to demonstrate how such a suppression of chaos may be understood in the framework of the effective ‘‘averaged’’ nonlinear equation for a slowly varying component of the oscillation amplitude. As follows from our numerical simulations, the suppression of chaos may be observed not only at large amplitudes of the parametric force but also at smaller amplitudes, showing a decay of the leading Lyapunov exponent within certain amplitude-frequency ‘‘windows.’’