Transition from quasiperiodicity to chaos in a Josephson-junction analog

Abstract

Experimental observations of the transition from quasiperiodicity to chaos are carried out with an electronic Josephson-junction simulator driven by two independent ac sources. A Poincar\'e section shows an invariant ellipse when the frequency ratio of the two input currents is very close to the reciprocal of the golden mean. The system enters a chaotic state at high input-current amplitudes characterized by a breakdown of the smooth ellipse at the onset of transition. Two convergence ratios are experimentally determined, showing good agreement with calculated values obtained by circle map studies.