Role of ultrasubharmonic resonances in taming chaos by weak harmonic perturbations

A general method is discussed concerning reduction of homoclinic and heteroclinic instabilities for a wide class of dissipative systems subjected to two small harmonic perturbations (one chaos-inducing and the other chaos-suppressing) which verify an ultrasubharmonic resonance condition: Ω/ω = p/q, q > 1 (p ≠ q), p,q positive integers and Ω(ω) the chaos-suppressing (inducing) frequency. The relevance of the theoretical findings on steady-chaos suppression is confirmed by means of Lyapunov exponent calculations of a Duffing oscillator.