IVC Calculation Problem for Josephson Junction Stacks.On Asymptotic Construction near the Breakpoint
Solving the system of essentially nonlinear diﬀerential equations for diﬀerent we obtain thecurrent-voltage characteristics (IVC) for a system of Josephson junctions (JJ) as a hysteresisloop. When the current approaches on the back way the breakpoint 𝐼𝑏the voltage (𝐼)falls sharply to zero. In addition, in numerical modelling (non-periodic boundary conditions(NPBC)) IVC multiple branching is observed near 𝐼𝑏. It is interesting to study this phenomenonanalytically developing asymptotic methods. There had been developed simple “asymptotic”formulas suitable for calculation of all IVC points except near to 𝐼𝑏. A numerical-analyticalmethod allowing to shorten IVC calculation time essentially was proposed. This method showedgood results in IVC multiple branching calculation in particular. All calculations were performedusing the REDUCE system. We succeeded ﬁrst to calculate analytically all points of IVC. Anapproximate solution at the breakpoint region (periodic boundary conditions (PBC)) has beendeveloped using the Bogolyubov-Krylov method.