Fractional order chaos in Josephson junction

Abstract

This paper studies the fractional-order chaotic dynamics of Josephson junction based on resistor and capacitor shunted junction (RCSJ) model proposed by W. C. Stewart and D. E. McCumber. The fractional-order numerical integration is carried out with modified trapezoidal rule. Fractional-order chaotic behaviors of the model are explained by bifurcation diagram. Numerical results confirm that there exists chaos at fractional-order in this model.   Key words: Fractional calculus, Josephson junction, chaotic dynamical system, numerical method.