SLOW PASSAGE THROUGH A HOMOCLINIC ORBIT WITH SUBHARMONIC RESONANCES

The slow passage through a homoclinic orbit is analyzed for a periodic ally forced and weakly damped strongly nonlinear oscillator correspond ing to a double-well potential. Multiphase averaging fails at an infin ite sequence of subharmonic resonance layers that coalesce on the homo clinic orbit. An accurate phase of the strongly nonlinear oscillator a fter passage through each subharmonic resonance is obtained using a ti me shift and a constant phase adjustment. Near the unperturbed homocli nic orbit, the solution is a large sequence of nearly homoclinic orbit s in which one saddle approach is mapped into the next. The method of matched asymptotic expansions is used to relate the solution in subhar monic resonance layers to the solution near the unperturbed homoclinic orbit. In this way, we determine an asymptotically accurate analytic description for the boundaries of the basins of attraction correspondi ng to capture into each well.