Analog computer simulation of the time-dependent Ginzburg-Landau equations used to describe dynamic properties of superconducting microbridges

We have simulated the dynamic behavior of a Josephson microbridge on the basis of the time-dependent Ginzburg-Landau equations using an analog computer. The current was the controlled parameter in these simulations. Our results are in agreement with previous investigations where digital computers were used. The speed and versatility of the analog computer allowed us to scan the solutions for a wide range of parameters. We have thus simulated a microbridge coupled to an external microwave source. The maximum step height in the I-V characteristic is larger than predicted by the resistively shunted junction model at low frequencies and smaller at higher frequencies. We have found parametric subharmonic generation on half the applied frequency on part of the induced step and for a certain power and frequency range. This remains to be investigated experimentally.