Bifurcation Phenomena in the Josephson Junction Circuit Coupled by a Resistor

Tetsushi UETA  Hiroshi KAWAKAMI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E79-A   No.10   pp.1546-1550
Publication Date: 1996/10/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications (NOLTA))
Category: Nonlinear Circuits and Bifurcation
Josephson junction,  pendulum,  frictional clutch,  bifurcation,  chaos,  

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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 Poincare mapping and obtain a bifurcation diagram. There are two types of limit cycles distinguished by whether the motion is in S1R3 or T2R2, 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.