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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Synchronization Dynamics of Modified Relay-coupled Chaotic Systems

Journal of Applied Nonlinear Dynamics 7(1) (2018) 11--24 | DOI:10.5890/JAND.2018.03.002

Patrick Louodop$^{1}$,$^{2}$, Elie B.Megam Ngouonkadi$^{2}$, Paulsamy Muruganandam$^{3}$, Hilda A. Cerdeira$^{1}$

$^{1}$ Instituto de Física Teórica - UNESP, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, Barra Funda, 01140-070 São Paulo, Brazil

$^{2}$ Laboratory of Electronics and Signal Processing, Faculty of Sciences, Department of Physics, University of Dschang, P.O. Box 67 Dschang, Cameroon

$^{3}$ Department of Physics, Bharathidasan University, Tiruchirapalli 620024, India

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Abstract

In this manuscript, we study the dynamics of a modified relay-coupled chaotic systems. The modification consists on the fact that the relay unit is modeled to lead the entire network to a desired dynamics. Then we achieve finite-time synchronization indirectly through a linear combination of the three systems. Further, we consider the existence of a switch on time of the coupling from the relay unit to the outer systems. It appears some interesting behaviors such as bifurcations, alternation of crisis and phases transitions when varied the switch on time. An open result is also found. In our scheme and for the selected changeable initial conditions, it seems that the appearance or disappearance of coexistence of attractors is linked to the type of synchronization we are dealing with. Mathematical demonstrations are given to sustain our theory while numerical simulations show its effectiveness.

Acknowledgments

H.A Cerdeira, P. Louodop and P.Muuganandam thank the ICTP-SAIFR and FAPESP grant 2011/11973-4 for partial financial support. P. L. acknowledges support by FAPESP grant 2014/13272-1.

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