Tetsushi Ueta, Hiroshi Kawakami, Bifurcation phenomena in the Josephson junction circuit coupled by a resistor, Institute of Electronics, Information and Communication Engineers, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E79-A, No.10, 1546-1550, Oct. 1996.
Abstract: Bifurcation phenomena observed in a circuit containing two Josephson junctions coupled by a resistor are investigated. This circuit model has a mechanical analogue; Two damped pendular linked by a clutch exchanging kinetic energy of each pendulum. In this paper, firstly we study equilibria of the system. Bifurcations and topological properties of the equilibria are clarified. Secondly we analyse periodic solutions in the system by using suitable Poincare mapping and obtain a bifurcation diagram. There are two types of limit cycles distinguished by whether the motion is in S1 * R3 or T2 * R2, since at most two cyclic coordinates are included in the state space. There is a typical structure of tangent bifurcation for 2-periodic solutions with a cusp point. We found chaotic orbits via the period-doubling cascade, and a long-period stepwise orbit.