Mapping of one-dimensional Josephson junction arrays onto cellular neural networks and their dynamics

It is shown that one-dimensional Josephson junction arrays can be mapped onto sworks under some restrictions. Analytic expressions to the stability of equilibria of these arrays are derived and applied to the behavior of vortex solutions. Relations between these static solutions and a particular solution of a partial differential equation are shown. By means of the theory of Hamiltonian systems, a qualitative theory for Josephson junction arrays is derived and applied in numerical simulations.