Generalized analytical solutions and experimental confirmation of complete synchronization in a class of mutually-coupled simple nonlinear electronic circuits

TL;DR

This paper derives explicit analytical solutions for synchronized states in coupled nonlinear electronic circuits, validates them through simulations and experiments, and provides conditions for stable synchronization.

Contribution

It introduces a generalized analytical solution for a class of coupled nonlinear circuits and confirms synchronization through experiments and stability analysis.

Findings

Analytical solutions for synchronization states are derived.

Experimental results confirm complete synchronization.

Stability conditions for synchronization are established.

Abstract

In this paper, we present a novel explicit analytical solution for the normalized state equations of mutually-coupled simple chaotic systems. A generalized analytical solution is obtained for a class of simple nonlinear electronic circuits with two different nonlinear elements. The synchronization dynamics of the circuit systems were studied using the analytical solutions. the analytical results thus obtained have been validated through numerical simulation results. Further, we provide a sufficient condition for synchronization in mutually-coupled, second-order simple chaotic systems through an analysis on the eigenvalues of the difference system. The bifurcation of the eigenvalues of the difference system as functions of the coupling parameter in each of the piecewise-linear regions, revealing the existence of stable synchronized states is presented. The stability of synchronized states are studied using the {\emph{Master Stability Function}}. Finally, the electronic circuit experimental results confirming the phenomenon of complete synchronization in each of the circuit system is presented.