Abstract and Applied Analysis
Volume 2013 (2013), Article ID 483269, 7 pages
http://dx.doi.org/10.1155/2013/483269
Effective Synchronization of a Class of Chua’s Chaotic Systems Using an Exponential Feedback Coupling
1Laboratory of Electronics, Department of Physics, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon
2Laboratory of Applied Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, P.O. Box 24157, Douala, Cameroon
3Instituto de Física Teórica-UNESP, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, Barra Funda, 01140-070 São Paulo, SP, Brazil
Received 17 February 2013; Accepted 4 March 2013
Academic Editor: René Yamapi
Copyright © 2013 Patrick Louodop et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Linked References
- L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- X. Li, X. Guan, and D. Ru, “The damping time of EEG with information retrieve and autoregressive models,” in Proceedings of the 5th IFAC Symposium on Modelling and Control in Biomedical Systems, Melbourne, Australia, August 2003.
- S. K. Han, C. Kurrer, and Y. Kuramoto, “Dephasing and bursting in coupled neural oscillators,” Physical Review Letters, vol. 75, no. 17, pp. 3190–3193, 1995. View at Publisher · View at Google Scholar · View at Scopus
- J. S. Lin, C. F. Huang, T. L. Liao, and J. J. Yan, “Design and implementation of digital secure communication based on synchronized chaotic systems,” Digital Signal Processing, vol. 20, no. 1, pp. 229–237, 2010. View at Publisher · View at Google Scholar · View at Scopus
- N. Islam, B. Islam, and H. P. Mazumdar, “Generalized chaos synchronization of unidirectionally coupled Shimizu-Morioka dynamical systems,” Differential Geometry, vol. 13, pp. 101–106, 2011. View at Google Scholar · View at MathSciNet
- B. Blasius, A. Huppert, and L. Stone, “Complex dynamics and phase synchronization in spatially extended ecological systems,” Nature, vol. 399, no. 6734, pp. 354–359, 1999. View at Publisher · View at Google Scholar · View at Scopus
- S. Sivaprakasam, I. Pierce, P. Rees, P. S. Spencer, K. A. Shore, and A. Valle, “Inverse synchronization in semiconductor laser diodes,” Physical Review A, vol. 64, no. 1, pp. 138051–138058, 2001. View at Google Scholar · View at Scopus
- I. Wedekind and U. Parlitz, “Synchronization and antisynchronization of chaotic power drop-outs and jump-ups of coupled semiconductor lasers,” Physical Review E, vol. 66, no. 2, Article ID 026218, pp. 1–4, 2002. View at Publisher · View at Google Scholar · View at Scopus
- A. Fradkov, H. Nijmeijer, and A. Markov, “Adaptive observer-based synchronization for communication,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 10, no. 12, pp. 2807–2813, 2000. View at Google Scholar · View at Scopus
- K. M. Cuomo and A. V. Oppenheim, “Circuit implementation of synchronized chaos with applications to communications,” Physical Review Letters, vol. 71, no. 1, pp. 65–68, 1993. View at Publisher · View at Google Scholar · View at Scopus
- S. Bowong, “Stability analysis for the synchronization of chaotic systems with different order: application to secure communications,” Physics Letters A, vol. 326, no. 1-2, pp. 102–113, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- S. Bowong and J. J. Tewa, “Unknown inputs' adaptive observer for a class of chaotic systems with uncertainties,” Mathematical and Computer Modelling, vol. 48, no. 11-12, pp. 1826–1839, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- H. Fotsin and S. Bowong, “Adaptive control and synchronization of chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators,” Chaos, Solitons and Fractals, vol. 27, no. 3, pp. 822–835, 2006. View at Publisher · View at Google Scholar · View at Scopus
- A. Astolfi, D. Karagiannis, and R. Ortega, Nonlinear and Adaptive Control with Applications, Springer, London, UK, 2008. View at MathSciNet
- G. Feng and R. Lozano, Adaptive Control Systems, Reed Elsevier, 1999.
- E. M. Shahverdiev, R. A. Nuriev, L. H. Hashimova, E. M. Huseynova, R. H. Hashimov, and K. A. Shore, “Complete inverse chaos synchronization, parameter mismatches and generalized synchronization in the multi-feedback Ikeda model,” Chaos, Solitons and Fractals, vol. 36, no. 2, pp. 211–216, 2008. View at Publisher · View at Google Scholar · View at Scopus
- V. Sundarapandian, “Global chaos anti-synchronization of Liu and Chen systems by nonlinear control,” International Journal of Mathematical Sciences & Applications, vol. 1, no. 2, pp. 691–702, 2011. View at Google Scholar · View at MathSciNet
- X. Zhang and H. Zhu, “Anti-synchronization of two different hyperchaotic systems via active and adaptive control,” International Journal of Nonlinear Science, vol. 6, no. 3, pp. 216–223, 2008. View at Google Scholar · View at MathSciNet
- H. Zhu, “Anti-synchronization of two different chaotic systems via optimal control with fully unknown parameters,” Information and Computing Science, vol. 5, pp. 11–18, 2010. View at Google Scholar
- X. Gao, S. Zhong, and F. Gao, “Exponential synchronization of neural networks with time-varying delays,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 71, no. 5-6, pp. 2003–2011, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- S. Zheng, Q. Bi, and G. Cai, “Adaptive projective synchronization in complex networks with time-varying coupling delay,” Physics Letters A, vol. 373, no. 17, pp. 1553–1559, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- J. Cai, M. Lin, and Z. Yuan, “Secure communication using practical synchronization between two different chaotic systems with uncertainties,” Mathematical & Computational Applications, vol. 15, no. 2, pp. 166–175, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- P. Louodop, H. Fotsin, and S. Bowong, “A strategy for adaptive synchronization of an electrical chaotic circuit based on nonlinear control,” Physica Scripta, vol. 85, no. 2, Article ID 025002, 2012. View at Publisher · View at Google Scholar
- M. Roopaei and A. Argha, “Novel adaptive sliding mode synchronization in a class of chaotic systems,” World Applied Sciences Journal, vol. 12, pp. 2210–2217, 2011. View at Google Scholar
- Z. Sun and X. Yang, “Parameters identification and synchronization of chaotic delayed systems containing uncertainties and time-varying delay,” Mathematical Problems in Engineering, vol. 2010, Article ID 105309, 15 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- S. T. Kammogne and H. B. Fotsin, “Synchronization of modified Colpitts oscillators with structural perturbations,” Physica Scripta, vol. 83, no. 6, Article ID 065011, 2011. View at Publisher · View at Google Scholar · View at Scopus
- C. K. Ahn, “Robust chaos synchronization using input-to-state stable control,” Pramana, vol. 74, no. 5, pp. 705–718, 2010. View at Publisher · View at Google Scholar · View at Scopus
- D. J. D. Earn, P. Rohani, and B. T. Grenfell, “Persistence, chaos and synchrony in ecology and epidemiology,” Proceedings of the Royal Society B, vol. 265, no. 1390, pp. 7–10, 1998. View at Publisher · View at Google Scholar · View at Scopus
- S. Bowong, “Optimal control of the transmission dynamics of tuberculosis,” Nonlinear Dynamics, vol. 61, no. 4, pp. 729–748, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- Z. Yang, G. K. M. Pedersen, and J. H. Pedersen, “Model-based control of a nonlinear one dimensional magnetic levitation with a permanent-magnet object,” in Automation and Robotics, chapter 21, pp. 359–374. View at Publisher · View at Google Scholar
- L. O. Chua, “The genesis of Chua's circuit,” AEU. Archiv fur Elektronik und Ubertragungstechnik, vol. 46, no. 4, pp. 250–257, 1992. View at Google Scholar · View at Scopus
- L. O. Chua, T. Yang, G. Q. Zhong, and C. W. Wu, “Synchronization of Chua's circuits with tune-varying channels and parameters,” IEEE Transactions on Circuits and Systems I, vol. 43, no. 10, pp. 862–868, 1996. View at Google Scholar · View at Scopus
- Y. Z. Yin, “Experimental demonstration of chaotic synchronization in the modified Chua's oscillators,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 7, no. 6, pp. 1401–1410, 1997. View at Google Scholar · View at Scopus
- X. X. Liao, H. G. Luo, G. Zhang, J. G. Jian, X. J. Zong, and B. J. Xu, “New results on global synchronization of Chua's circuit,” Acta Automatica Sinica, vol. 31, no. 2, pp. 320–326, 2005. View at Google Scholar · View at Scopus
- A. Y. Markov, A. L. Fradkov, and G. S. Simin, “Adaptive synchronization of chaotic generators based on tunnel diodes,” in Proceedings of the 35th IEEE Conference on Decision and Control, pp. 2177–2182, December 1996. View at Scopus
- Z. Ding and G. Cheng, “A new uniformly ultimate boundedness criterion for discrete-time nonlinear systems,” Applied Mathematics, vol. 2, pp. 1323–1326, 2011. View at Google Scholar
- M. de la Sen and S. Alonso, “Adaptive control of time-invariant systems with discrete delays subject to multiestimation,” Discrete Dynamics in Nature and Society, vol. 2006, Article ID 41973, 27 pages, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- G. Bitsoris, M. Vassilaki, and N. Athanasopoulos, “Robust positive invariance and ultimate bounded- ness of nonlinear systems,” in Proceedings of the 20th Mediterranean Conference on Control and Automation (MED), pp. 598–603, Barcelona, Spain, July 2012.