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Boundary of the basin of attraction for weakly damped primary resonance. (English) Zbl 0845.70017

Summary: The dissipatively perturbed Hamiltonian system corresponding to primary resonance is analyzed in the case in which two competing stable periodic responses exist. By using the small dissipation of the Hamiltonian (the Melnikov integral) near the homoclinic orbit, the boundaries of the basin of attraction are determined analytically in an asymptotically accurate way. The selection of the two competing periodic responses is influenced by small changes in the initial conditions. The analytic formula agrees will with numerical computations.

MSC:

70K30 Nonlinear resonances for nonlinear problems in mechanics
70K50 Bifurcations and instability for nonlinear problems in mechanics
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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