- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 483269, 7 pages
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.
- L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- A. Astolfi, D. Karagiannis, and R. Ortega, Nonlinear and Adaptive Control with Applications, Springer, London, UK, 2008.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- C. K. Ahn, “Robust chaos synchronization using input-to-state stable control,” Pramana, vol. 74, no. 5, pp. 705–718, 2010.
- 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.
- S. Bowong, “Optimal control of the transmission dynamics of tuberculosis,” Nonlinear Dynamics, vol. 61, no. 4, pp. 729–748, 2010.
- 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.
- L. O. Chua, “The genesis of Chua's circuit,” AEU. Archiv fur Elektronik und Ubertragungstechnik, vol. 46, no. 4, pp. 250–257, 1992.
- 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.
- 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.
- 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.
- 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.
- Z. Ding and G. Cheng, “A new uniformly ultimate boundedness criterion for discrete-time nonlinear systems,” Applied Mathematics, vol. 2, pp. 1323–1326, 2011.
- 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.
- 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.