Role of ultrasubharmonic resonances in taming chaos by weak harmonic perturbations

A general method is discussed concerning reduction of homoclinic and hetero clinic instabilities for a wide class of dissipative systems subjected to t wo small harmonic perturbations (one chaos-inducing and the other chaos-sup pressing) which verify an ultrasubharmonic resonance condition: Omega/omega = p/q, q > 1(p not equal q), p,q positive integers and Omega(omega) the ch aos-suppressing (inducing) frequency. The relevance of the theoretical find ings on steady-chaos suppression is confirmed by means of Lyapunov exponent calculations of a Duffing oscillator.