Synchronization in hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment

TL;DR

This paper demonstrates experimentally and analytically how hyperchaotic time-delayed electronic oscillators can synchronize in various phases through indirect coupling via a common environment, with results supported by numerical analysis.

Contribution

First experimental confirmation of hyperchaos synchronization in time-delayed electronic oscillators coupled indirectly through a common environment.

Findings

In-phase and inverse-phase synchronization observed experimentally.

Transition from partial to complete synchronization with increasing coupling strength.

Numerical Lyapunov spectrum confirms synchronization transitions.

Abstract

The present paper explores the synchronization scenario of hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment. We show that depending upon the coupling parameters a hyperchaotic time-delayed system can show in-phase or complete synchronization, and also inverse-phase or anti-synchronization. This paper reports the first experimental confirmation of synchronization of hyperchaos in time-delayed electronic oscillators coupled indirectly through a common environment. We confirm the occurrence of in-phase and inverse-phase synchronization phenomena in the coupled system through the dynamical measures like generalized autocorrelation function, correlation of probability of recurrence, and the concept of localized sets computed directly from the experimental time-series data. We also present a linear stability analysis of the coupled system. The experimental and analytical results are further supported by the detailed numerical analysis of the coupled system. Apart from the above mentioned measures, we numerically compute another quantitative measure, namely, Lyapunov exponent spectrum of the coupled system that confirms the transition from the in-phase (inverse-phase) synchronized state to the complete (anti-) synchronized state with the increasing coupling strength.