Synchronization transitions in coupled time-delay electronic circuits with a threshold nonlinearity

TL;DR

This paper experimentally and numerically investigates synchronization transitions in coupled time-delay electronic circuits with threshold nonlinearity, revealing how different synchronization types depend on delays and coupling, with a unified stability condition.

Contribution

It demonstrates the existence of various synchronization transitions in coupled time-delay circuits and establishes a delay-independent stability criterion, supported by experiments and numerical analysis.

Findings

Transitions from anticipatory to lag synchronization observed

A single stability condition valid for all synchronization types

Numerical simulations confirm experimental results

Abstract

Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay $\tau_1$ and coupling delay $\tau_2$. We have observed transitions from anticipatory to lag via complete synchronization and their inverse counterparts with excitatory and inhibitory couplings, respectively, as a function of the coupling delay $\tau_2$. The anticipating and lag times depend on the difference between the feedback and the coupling delays. A single stability condition for all the different types of synchronization is found to be valid as the stability condition is independent of both the delays. Further, the existence of different kinds of synchronizations observed experimentally is corroborated by numerical simulations, and from the changes in the Lyapunov exponents of the coupled time-delay systems.