L. Finger et V. Tavsanoglu, MAPPING OF ONE-DIMENSIONAL JOSEPHSON-JUNCTION ARRAYS ONTO CELLULAR NEURAL NETWORKS AND THEIR DYNAMICS, IEEE transactions on circuits and systems. 1, Fundamental theory andapplications, 44(5), 1997, pp. 438-445
In this brief, it is shown that one-dimensional Josephson junction arr
ays can be mapped onto sworks under some restrictions. Analytic expres
sions to the stability of equilibria of these arrays are derived and a
pplied to the behavior of vortex solutions. Relations between these st
atic solutions and a particular solution of a partial differential equ
ation are shown. By means of the theory of Hamiltonian systems a quali
tative theory for Josephson junction arrays is derived and applied in
numerical simulations.