Estudio de los exponentes de Lyapunov para un sistema de n-junturas Josephson

Abstract

In the past years, many applications of superconductivity have been developed thanks to the Josephson junction. This junction is a union formed by two superconducting films separated by an insulating material that is used, among many other applications, to define voltage “standards” in physics and to encrypt images in telecommunication systems. The correct operation of these two applications depends on the values of certain parameters of the junction, values that define a parameter space where each point of this space causes different dynamic properties of the system. When the dynamic is non-chaotic, the junction allows to establish constant voltages -which are used as voltage standards-, while when the dynamic is chaotic, the junction allows to define encryption

mechanisms. To classify the chaotic and non-chaotic dynamics for different zones in the parameter space we have used the Lyapunov exponents, through which we have found zones that produce constant voltages and zones that produces chaotic dynamics that, in addition, we have characterized through the Kolmogorov entropy and the Kaplan-Yorke dimension. Some of the results obtained reproduce previously observations established in the literature.