Phase effects on synchronization by dynamical relaying in delay-coupled systems

TL;DR

This paper investigates how phase differences and time delays influence synchronization in delay-coupled Josephson junction systems, revealing the effects of damping, coupling, and detuning on system dynamics.

Contribution

It introduces a detailed analysis of phase effects on synchronization in delay-coupled systems using Josephson junctions, including Lyapunov exponents and numerical studies.

Findings

Synchronization depends on damping, coupling, and delay parameters.

Time-delay and phase difference significantly alter system dynamics.

Small frequency detuning impacts synchronization stability.

Abstract

Synchronization in an array of mutually coupled systems with a finite time-delay in coupling is studied using Josephson junction as a model system. The sum of the transverse Lyapunov exponents is evaluated as a function of the parameters by linearizing the equation about the synchronization manifold. The dependence of synchronization on damping parameter, coupling constant and time-delay is studied numerically. The change in the dynamics of the system due to time-delay and phase difference between the applied fields is studied. The case where a small frequency detuning between the applied fields is also discussed.