BOUNDARY OF THE BASIN OF ATTRACTION FOR WEAKLY DAMPED PRIMARY RESONANCE

The dissipatively perturbed Hamiltonian system corresponding to primar y resonance is analyzed in the case in which two competing stable peri odic responses exist. The method of averaging fails as the trajectory approaches the unperturbed homoc2inic orbit (separatrix). By using the small dissipation of the Hamiltonian (the Melnikov integral) near the homoclinic orbit, the boundaries of the basin of attraction are deter mined analytically in an asymptotically accurate way. The selection of the two competing periodic responses is influenced by small changes i n the initial conditions. The analytic formula is shown to agree well with numerical computations.