General results on chaos suppression for biharmonically driven dissipativesystems

General results concerning suppression of homoclinic (and heteroclinic) cha os are derived on the basis of a Melnikov analysis for damped, nonlinear, a nd low-dimensional oscillators subjected to two weak harmonic excitations ( one chaos-inducing and the other chaos-suppressing). Analytical expressions are deduced for the intervals of initial phase difference between the two excitations for which chaotic dynamics can be eliminated. It is demonstrate d that {0, pi/2, pi ,3 pi/2} are, in general, the only optimal values of su ch phase differences, in the sense that they allow the widest amplitude ran ges for the chaos-suppressing excitation. (C) 1999 Published by Elsevier Sc ience B.V. All rights reserved.