A CODIMENSION-2 POINT ASSOCIATED WITH COUPLED JOSEPHSON-JUNCTIONS

The dynamics of a pair of identical Josephson junctions coupled throug h a shared purely capacitive load are governed by a two-parameter syst em of two second-order nonlinear ordinary differential equations. Nume rical simulations have shown that this system possesses many different running and periodic solutions. Continuation studies using AUTO indic ate that many of these solution branches are generated by a codimensio n-2 connection which occurs at a particular parameter point. In this p aper, we first describe these calculations in detail. We then study a general two-parameter system whose properties reflect some of those fo und in our numerical studies of the Josephson junction system. In part icular, our model system is assumed to possess an appropriate codimens ion-2 connection, and we prove that its unfolding generates a large va riety of codimension-1 connection curves. These results, combined with the particular symmetry and periodicity properties of the junction eq uations, account for all of the numerically observed solution branches . Indeed, the theoretical analysis predicted the existence of branches which were not initially observed, but which were subsequently found.