Resonant regions of Josephson junction equation in case of large damping. (English) Zbl 1220.81181
Summary: The dynamics of Josephson junction equation in case of damping \(\alpha >2\) is investigated numerically. In this case the second-order system can be asymptotically reduced in the large to a one-dimensional circle map. We study the parametric dependence of the resonances of this system and plot the resonant regions in two-dimensional parameter space. The periodic variation of the widths of harmonic regions with increase of the periodic driving force is observed. In the limit of infinite damping, we study a first order system through suitable re-scaling and the same property is observed. We conjecture this may caused by the competition between the periodic potential and the periodic external driving in these systems.
MSC:
81V10 | Electromagnetic interaction; quantum electrodynamics |
82D55 | Statistical mechanics of superconductors |
55M25 | Degree, winding number |
82C80 | Numerical methods of time-dependent statistical mechanics (MSC2010) |
37L10 | Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems |
70K28 | Parametric resonances for nonlinear problems in mechanics |
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