Dynamic environment coupling induce synchronized states in coupled time-delayed electronic circuits

TL;DR

This paper experimentally demonstrates how dynamic environment coupling induces various synchronized states in coupled time-delayed electronic circuits, with analysis supported by numerical simulations and stability conditions.

Contribution

It introduces a novel experimental approach using dynamic environment coupling to induce and analyze synchronization in hyperchaotic circuits.

Findings

Different synchronized states observed, including complete, phase, and inverse synchronization.

Transitions between synchronization states depend on coupling strength and feedback nature.

Stability analysis provides conditions for the emergence of these states.

Abstract

We experimentally demonstrate the occurrence of various synchronized states in coupled piece-wise linear time-delayed electronic circuits using dynamic environment coupling where the environment has its own intrinsic dynamics via feedback from the circuits. We carry out these experiments in two different coupling configurations, namely mutual and subsystem coupling configurations. Depending upon the coupling strength and the nature of feedback, we observe a transition from nonsynchronization to complete synchronization via phase synchronization and from nonsynchronization to inverse synchronization via inverse-phase synchronization between the circuits in hyperchaotic regime. Snapshots of the time evolution, phase projection plots and localized sets of the circuits as observed experimentally from the oscilloscope, along with supporting numerical simulations confirm the existence of different synchronized states. Further, the transition to different synchronized states can be verified from the changes in the largest Lyapunov exponents, Correlation of Probability of Recurrence and Correlation Coefficient as a function of the coupling strength. We present a detailed linear stability analysis and obtain conditions for different synchronized states.