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Talk Abstract

Dynamics of Josephson Junctions Coupled through a Shared LRC-Load

Dynamics of Josephson Junctions Coupled through a Shared LRC-Load

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.