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Nonlinear Sciences > Chaotic Dynamics

arXiv:1709.04132 (nlin)
[Submitted on 13 Sep 2017]

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

Authors:G. Sivaganesh, A. Arulgnanam, A.N. Seethalakshmi
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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.
Comments: 12 pages, 6 figures. arXiv admin note: text overlap with arXiv:1611.04289
Subjects: Chaotic Dynamics (nlin.CD)
Cite as: arXiv:1709.04132 [nlin.CD]
  (or arXiv:1709.04132v1 [nlin.CD] for this version)
  https://doi.org/10.48550/arXiv.1709.04132
Journal reference: Chaos Solitons & Fractals, Vol. 113, 2018
Related DOI: https://doi.org/10.1016/j.chaos.2018.06.001

Submission history

From: G Sivaganesh [view email]
[v1] Wed, 13 Sep 2017 04:27:14 UTC (1,498 KB)
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