Calculation of period doubling in a Josephson circuit

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Abstract
The method of harmonic balance is used to obtain analytic results for the differential equation describing a current-biased Josephson junction with self-capacitance that is shunted by a resistor with substantial self-inductance. This system is known to exhibit period-doubling cascades, chaos, and other exotic nonlinear phenomena. After an accurate representation of the basic voltage oscillation is determined for high-bias currents, the value of bias current is computed for which this solution loses stability to a period-doubled mode. The predictions agree to remarkable accuracy with results obtained from both analog simulations and digital integration of the circuit equation, typically 5% for moderate values of inductance. Moreover, the method of calculation provides a systematic scheme for achieving increasing accuracy.