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SUMMARYIn some electronic systems, such as cryoelectronic circuits, random noise has to be taken into consideration for modelling and simulation. After theoretical considerations an algorithm for the simulation of non-linear circuits with random noise is developed. Methods for global analysis of non-linear dynamical systems, such as Lyapunov exponents and the Poincad map, are applied to systems with noise. The developed algorithms are applied to the cryoelectronic circuit of the ideal DC-SQUID model. Several non-linear effects which occur through noise are explained.

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In this paper it is shown that one-dimensional Josephson junction arrays can be mapped onto Cellular Neural Networks under some restrictions. Analytic expressions to the stability of equilibria of these arrays are derived and applied to the behavior of vortex solutions. Relations between these static solutions and a particular solution of a partial differential equation are shown.

An enhancement of the classical Runge—Kutta technique for numerical simulations is presented for the computer-aided global analysis of nonlinear dynamic circuits/systems. With Runge—Kutta triples a remarkable saving of calculation time can be achieved by using an interpolation polynomial for dense output. The Runge—Kutta triples are applied to calculate the Poincaré map for autonomous models/systems.