Repeated Resonance and Homoclinic Bifurcation in a Periodically Forced Family of Oscillators

Abstract

We use global perturbation techniques originally due to Melnikov [1963] to study the bifurcation behavior exhibited by a family of nonlinear oscillators subject to periodic forcing. We concentrate on the case in which the unforced systems possess a one-parameter family of periodic orbits limiting on a homoclinic orbit.