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Generalized analytical solutions and experimental confirmation of complete synchronization in a class of mutually coupled simple nonlinear electronic circuits
- Source :
- Chaos, Solitons & Fractals. 113:294-307
- Publication Year :
- 2018
- Publisher :
- Elsevier BV, 2018.
-
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.<br />12 pages, 6 figures. arXiv admin note: text overlap with arXiv:1611.04289
- Subjects :
- Computer simulation
General Mathematics
Applied Mathematics
Synchronization of chaos
FOS: Physical sciences
General Physics and Astronomy
Statistical and Nonlinear Physics
Fixed point
Nonlinear Sciences - Chaotic Dynamics
01 natural sciences
Stability (probability)
Synchronization
010305 fluids & plasmas
Nonlinear system
Control theory
0103 physical sciences
Applied mathematics
Chaotic Dynamics (nlin.CD)
010306 general physics
Eigenvalues and eigenvectors
Master stability function
Mathematics
Subjects
Details
- ISSN :
- 09600779
- Volume :
- 113
- Database :
- OpenAIRE
- Journal :
- Chaos, Solitons & Fractals
- Accession number :
- edsair.doi.dedup.....bad5ffaab5b257ec7ddcd82567f1c574