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

Abstract

A novel generalized analytical solution for the normalized state equations of a class of mutually coupled chaotic systems is presented. To the best of our knowledge, for the first time synchronization dynamics of mutually coupled chaotic systems is studied analytically. The coupled dynamics obtained through the analytical solutions has been validated by numerical simulation results. Furthermore, we provide a suitable condition for the occurrence of synchronization in mutually coupled, second-order, non-autonomous chaotic systems through the analysis of the difference system on the stability of fixed points. The bifurcation of the eigenvalues of the difference system as a function 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 in each coupled system discussed in this article is studied using the Master Stability Function. Finally, the electronic circuit experimental results confirming the analytical and numerical results are presented.