Josephsonjunction circuit analysis via integral manifolds
Abstract
Using a secondorder circuit model the complex dynamical behavior of a typical Josephsonjunction circuit is rigorously analyzed using integral manifolds. The key idea is to prove that under certain smallparameter assumptions, the nonautonomous circuit has a stable integral manifold. Moreover, this manifold is doubly periodic so that steadystate behavior of the Josephsonjunction circuit reduces to the analysis of its dynamics on a torus. Wellknown experimental phenomena, such as the existence of hysteresis in the dc Josephson circuit and voltage steps in the ac Josephson circuit, are rigorously derived and explained.
 Publication:

IEEE Transactions on Circuits Systems
 Pub Date:
 May 1983
 Bibcode:
 1983ITCS...30..308C
 Keywords:

 Alternating Current;
 Circuits;
 Direct Current;
 Josephson Junctions;
 Manifolds (Mathematics);
 Network Analysis;
 VoltAmpere Characteristics;
 Dynamic Characteristics;
 Numerical Analysis;
 Poincare Problem;
 Steady State;
 Toruses;
 Electronics and Electrical Engineering