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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.
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Ricardo Chacón (2001) studied this question.
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