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Talk Abstract
Dynamics of Josephson Junctions Coupled through a Shared LRC-Load

Don Aronson, University of Minnesota

We consider a system of N identical current-biased Josephson point junctions coupled via a shared LCR-load. The mathematical midel involves a system of N "pendulum-type" equations with a load-induced forcing term together with a second-order load equation which is forced by the mean velocity of the pendula. In addition to the three load parameters, the system involves two additional parameters describing the intrinsic capacity of the junctions and the common bias current. The system is equivariant with respect to permutations and is consequently amenable to a considerable amount of analysis. Numerical studies for specific loads have shown that the system has extremely complicated dynamics. We will describe some of these observations, and show how continuation studies using AUTO together with geometrical and classical analysis have led to a nearly complete picture of the dynamics in certain cases. Much work remains to be done and there are many open problems. One of the main open problems involves the singular limit in which the individual junction capacities tend to zero.

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