Analysis of three non-identical Josephson junctions by the method of Lyapunov exponents charts

TL;DR

This paper investigates the complex dynamics of three non-identical Josephson junctions connected through an RLC circuit using Lyapunov exponents charts, revealing various invariant tori and bifurcation phenomena.

Contribution

It introduces the application of Lyapunov exponents charts to analyze the dynamics and bifurcations in a system of non-identical Josephson junctions with different coupling types.

Findings

Identification of main dynamic regimes using Lyapunov charts

Demonstration of two and three-frequency invariant tori

Analysis of saddle-node bifurcations of resonant tori

Abstract

A system of three non-identical Josephson junctions connected via an RLC circuit is considered. The method of Lyapunov exponents charts is used, which makes it possible to identify the main types of dynamics of the system and to analyze the dependence of its properties on parameters. The possibility of both two and three-frequency invariant tori is demonstrated. Saddle-node bifurcations of resonant tori are studied with the use of instantaneous Lyapunov exponents. The dependence of the charts on the type of coupling in the system is discussed.