FREQUENCY LOCKING IN JOSEPHSON ARRAYS - CONNECTION WITH THE KURAMOTO MODEL

The circuit equations for certain series arrays of Josephson junctions can be mapped onto a simple model originally introduced by Kuramoto [ in Proceedings of the International Symposium on Mathematical Problems in Theoretical Physics, edited by H. Araki, Lecture Notes in Physics Vol. 39 (Springer, Berlin, 1975)] to study fundamental aspects of freq uency locking in large populations of nonlinear oscillators. This corr espondence makes it possible to derive accurate theoretical prediction s of transitions signaling the onset of partial and complete locking, respectively. We calculate that both transitions should be observable experimentally using present fabrication tolerances. [S1063-651X(98)06 102-9].