Dynamics of two capacitively coupled Josephson junctions in the overdamped limit

T.P. Valkering, C.L.A. Hooijer, M.F. Kroon

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    The dynamics of two capacitively coupled Josephson junctions are investigated analytically and numerically on the basis of the RSJ-model. The attention is focussed on nearly identical junctions with zero internal capacitance, the so-called overdamped limit. This is a common assumption for high-Tc junctions. Varying one of the control currents the dynamics shows the typical phenomenon of frequency locking and the corresponding devil’s staircase for a relevant range of system parameters and upper bounds for the widths of the locking regions in terms of the control currents are derived. Correspondingly, closer inspection reveals that below a certain value of the coupling capacitance the dynamics takes place on a two-dimensional torus in the phase space. Numerical evidence is found from the calculation of Poincaré sections, and more definitely, from Lyapunov exponents. Using the concept of normal hyperbolicity, a proof of the existence of an attracting two-torus is given. Above this value the torus and the devil’s staircase partially break up and chaotic dynamics appear in between the main steps of the staircase.
    Original languageUndefined
    Pages (from-to)137-153
    Number of pages17
    JournalPhysica D
    Issue number135
    Publication statusPublished - 2000


    • Torus breakup
    • Frequency locking
    • IR-58905
    • Josephson junction
    • METIS-128731
    • High-Tc

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