Abstract
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 the voltage ()falls sharply to zero. In addition, in numerical modelling (non-periodic boundary conditions(NPBC)) IVC multiple branching is observed near . 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 . 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.
Highlights
The definition of the singular points of the current voltage characteristics together with the estimation of the width of their influence region provide adequate input for physical experiments aiming at studying the finite Josephson junctions (JJ) stacks [1,2,3]
The mathematical problem of I we obtain the current-voltage characteristics (IVC) calculation for the stack of n Josephson junction [4] asks for the solution of the following essentially nonlinear system: n φl = Al,l′ (I − sin(φl′ ) − βφl′ ), l = 1, . . . , n
This shortens the time of IVC calculation complimentarily
Summary
The definition of the singular points of the current voltage characteristics together with the estimation of the width of their influence region provide adequate input for physical experiments aiming at studying the finite JJ stacks [1,2,3]. In the case of PBC A is symmetric square matrix of order n: Received 25th July, 2017. In the case of NPBC A is symmetric square tridiagonal matrix of order n:. The dynamics of phase differences φl(t) had been simulated [4] by solving the equation system (1) using the fourth order Runge–Kutta method. This shortens the time of IVC calculation complimentarily
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