Bifurcation Phenomena in the Josephson Junction Circuit Coupled by a Resistor (Special Section on Nonlinear Theory and its Applications)

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 pendula 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 analyze periodic solutions in the system by using suitable Poincaré 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 ia 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.

(c)1996 The Institute of Electronics, Information and Communication Engineers
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