CFP last date
15 May 2024
Reseach Article

Adaptive Synchronization between Different Chaotic Systems with Unknown Parameters

Published on June 2013 by M. Srivastava, S. K. Agrawal, V. Mishra
International Conference and workshop on Advanced Computing 2013
Foundation of Computer Science USA
ICWAC - Number 1
June 2013
Authors: M. Srivastava, S. K. Agrawal, V. Mishra
741bd058-f9f4-4ec1-9927-c4015e8d65c2

M. Srivastava, S. K. Agrawal, V. Mishra . Adaptive Synchronization between Different Chaotic Systems with Unknown Parameters. International Conference and workshop on Advanced Computing 2013. ICWAC, 1 (June 2013), 0-0.

@article{
author = { M. Srivastava, S. K. Agrawal, V. Mishra },
title = { Adaptive Synchronization between Different Chaotic Systems with Unknown Parameters },
journal = { International Conference and workshop on Advanced Computing 2013 },
issue_date = { June 2013 },
volume = { ICWAC },
number = { 1 },
month = { June },
year = { 2013 },
issn = 2249-0868,
pages = { 0-0 },
numpages = 1,
url = { /proceedings/icwac/number1/472-1301/ },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Proceeding Article
%1 International Conference and workshop on Advanced Computing 2013
%A M. Srivastava
%A S. K. Agrawal
%A V. Mishra
%T Adaptive Synchronization between Different Chaotic Systems with Unknown Parameters
%J International Conference and workshop on Advanced Computing 2013
%@ 2249-0868
%V ICWAC
%N 1
%P 0-0
%D 2013
%I International Journal of Applied Information Systems
Abstract

This article deals with synchronization between different chaotic systems such as Genesio-Tesi and Qi system using adaptive control method. Based on Lyapunov stability theory, the synchronization between a pair of chaotic systems with fully unknown parameters is derived. An adaptive control law and a parameter update rule for unknown parameters are designed such that the chaotic Qi system is controlled to be the chaotic Genesio-Tesi system. Numerical simulation results which are carried out using MATLAB, show that the adaptive control method is effective, easy to implement and reliable for synchronizing of the considered chaotic systems.

References
  1. Alligood, K. T. , Sauer, T. , Yorke, J. A. : Chaos: An Introduction to Dynamical Systems. Springer-Verlag, Berlin (1997).
  2. Pecora, L. M. , Carroll, T. L. : Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821- 824 (1990).
  3. Ott, E. , Grebogi, C. , Yorke, J. A. : Controlling chaos. Phys. Rev. Lett. 64, 1196-1199 (1990).
  4. Chen, G. , Dong, X. : From Chaos to Order: Methodologies, Perspectives and Applications. World Scientific, Singapore (1998).
  5. Fuh, C. C. , Tung, P. C. : Controlling chaos using differential geometric method. Phys. Rev. Lett. 75, 2952-2955(1995).
  6. Chen, G. , Dong, X. : On feedback control of chaotic continuous-time systems. IEEE Trans. Circuits Systems. 40, 591-601 (1993).
  7. Blasius, B. , Huppert, A. , Stone, L. : Complex dynamics and phase synchronization in spatially extended ecological system. Nature 399, 354-359 (1999).
  8. Lakshmanan, M. , Murali, K. : Chaos in Nonlinear Oscillators: Controlling and Synchronization. World Scientific, Singapore (1996).
  9. Han, S. K. , Kerrer, C. , Kuramoto, Y. : D-phasing and bursting in coupled neural oscillators. Phys. Rev. Lett. 75, 3190-3193 (1995).
  10. Cuomo, K. M. , Oppenheim, A. V. : Circuit implementation of synchronized chaos with application to communication. Phys. Rev. Lett. 71, 65-68 (1993).
  11. Kocarev, L. , Parlitz, U. : General approach for chaotic synchronization with applications to communication. Phys. Rev. Lett. 74,5028- 5030 (1995).
  12. Murali, K. , Lakshmanan, M. : Secure communication using a compound signal using sampled-data feedback. Appld. Math. Mech. 11, 1309-1315 (2003).
  13. Park, J. H. , Kwon, O. M. : A novel criterion for delayed feedback control of time-delay chaotic systems. Chaos, Solitons& Fractals 23, 495-501 (2005).
  14. Zhang, H. , Huang, W. , Wang, Z. , Chai, T. : Adaptive synchronization between two different chaotic systems. Phys. Lett. A 350, 363–366 (2006).
  15. Hu, J. , Chen, S. , Chen, L. : Adaptive control for anti-synchronization of Chua's chaotic System. Phys. Lett. A 339, 455–460 (2005).
  16. Salarieha, H. , Shahrokhi, M. : Adaptive synchronization of two different chaotic systems with time varying unknown parameters. Chaos, Solitons& Fractals 37, 125–136 (2008).
  17. Wu, X. , Guan, Z. , Wu, Z. : Adaptive synchronization between two different hyperchaotic Systems. Nonlin. Anal. 68, 1346-1351 (2008).
  18. Zhang, X. , Zhu, H. : Anti-synchronization of two different hyperchaotic systems via active and adaptive control. Int. J. Nonlin. Sci. 6, 216-223 (2008).
  19. Mossa Al-sawalha, M. , Noorani, M. S. M. , Al-dlalah, M. M. : Adaptive anti- synchronization of chaotic systems with fully unknown parameters. Comput. and Math. withApplic. 59 3234-3244 (2010).
  20. Zhu, Q. , Cao, J. : Adaptive synchronization of chaotic Cohen–Crossberg neural networks with systems mixed time delays. Nonlin. Dyn. 61, 517-534 (2010).
  21. Mossa Al-sawalha, M. , Noorani, M. S. M. : Adaptive anti-synchronization of two identical and different hyperchaotic systems with uncertain parameters, Commun. Nonlin. Sci. Numer. Simulat. 15, 1036–1047 (2010).
  22. Li, X. -F. , Leung, A. C. -S. , Han, X. P. , Liu, X. -J. , Chu, Y. -D. : Complete (anti-) synchronization of chaotic systems with fully uncertain parameters by adaptive control. Nonlin. Dyn. 63,263-275 (2011).
  23. Yassen, M. T. : Chaos synchronization between two different chaotic systems using active Control. Chaos, Solitons& Fractals 23, 131-140 (2005).
  24. Chen, D. , Zhang, R. , Ma, X. , Liu, S:Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic systems via a sliding mode control scheme. Nonlin. Dyn. 69, 35–55 (2012). DOI: 10. 1007/s11071- 011-0244-7
  25. Yu, H. J. , Liu, Y. Z. : Chaotic synchronization based on stability criterion of linear systems. Phys. Lett. A 314, 292–298 (2003).
  26. Rosenblum, M. G. , Pikovsky, A. S. , Kurths, J. : From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett. 78, 4193–4196 (1997).
  27. Mahmoud, G. M. , Mahmoud, E. E. : Phase and anti-phase synchronization of two identical hyperchaotic complex nonlinear systems. Nonlin. Dyn. 61, 141–152 (2010).
  28. Wang, Z-L, Shi, X-R : Anti-synchronization of Liu system and Lorenz system with known or unknown parameters. Nonlin. Dyn. 57, 425-430 (2009).
  29. Ghosh, D. , Bhattacharya, S. : Projective synchronization of new hyperchaotic system withfully unknown parameters. Nonlin. Dyn. 61, 11–21 (2010).
  30. Genesio, R. , Tesi, A. : A harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems. Automatica 28, 531–548 (1992).
  31. G. Qi, G. R. Chen, S. Du, Z. Chen and Z. Yuan, Analysis of a new chaotic system, Physica A 352,295–308(2005).
Index Terms

Computer Science
Information Sciences

Keywords

Chaos Synchronization Genesio-Tesi system Qi system Adaptive control method