Abstract
Effective numerical algorithms are worked out for solving the nolinear system of ODE for finding the static distributions of the magnetic flux in N-stacked JJs, as well as the corresponding matrix Sturm-Liouville problem for studying their global stability. The particular case of three stacked JJs is investigated. A correspondence is made between loss of stability of a possible static distribution of the magnetic flux, obtained by solving the static problem, and the switching to dynamic state obtained by solving the dynamic problem. In this work we show by means of numerical simulation that the transient process of switching from static to dynamic state in symmetric three stacked JJs depends on the way of exceeding the external current.
Highlights
Stacks of long Josephson Junctions (JJs) were intensively studied during the past years
NUMERICAL RESULTS The simplest generalizable model of stacked JJs is the case of three stacked JJs because it takes into account the difference in the behavior of the interior and exterior junctions
The numerical results presented here are for the particular case of three stacked JJs, but the method of investigation and its program realization are developed for the general N-junction case (N > 1)
Summary
Stacks of long Josephson Junctions (JJs) were intensively studied during the past years. In these systems both nonlinearity and interaction between subsystems play an important role Such structures make it possible to state and study new physical effects that do not occur in single JJs. One of the most interesting experimental results for two stacked JJs found in resent years is the so-called current locking (CL). One of the most interesting experimental results for two stacked JJs found in resent years is the so-called current locking (CL) The essence of this phenomenon is as follows: there exists a range of the external magnetic field where the different junctions switch to dynamic state simultaneously when the external current exceeds some critical value. For example we can interpret the transitions from static to dynamic state as bifurcations of some stable static solutions under the change of parameters (the applied magnetic field and the external current)
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