Numerical investigation of the magnetic flux static distributions in layered josephson junctions

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.