Skip to main content
SpringerLink
Log in

Synchronization of Chaotic Neural Networks: A Generalized Hamiltonian Systems Approach

  • Chapter
Hybrid Intelligent Systems

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 208))

  • 816 Accesses

Abstract

to synchronize chaotic neural networks unidirectionally coupled. Synchronization is thus between the master and the slave networks with the slave network being given by an observer. In this paper, we use a Generalized Hamiltonian forms approach

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aguilar, A. and Cruz-Hernández, C. (2002) “Synchronization of two hyperchaotic Rössler systems: Model matching approach, “WSEAS Trans. Systems 1(2), 198–203.

    Google Scholar 

  2. Chua, L.O. and Yang, L. (1988) “Cellular neural networks: Theory and applications,” IEEE Trans. Circuits Syst. I 35, 1257–1290.

    Article  MATH  Google Scholar 

  3. Chua, L.O. (1998) CNN: A Paradigm for Complexity, World Scientific, Singapore.

    MATH  Google Scholar 

  4. Cruz-Hernández, C. and Nijmeijer, H. (1999) “Synchronization through extended Kalman filtering,” New Trends in Nonlinear Observer Design eds. Nijmeijer & Fossen, Lecture Notes in Control and Information Sciences 244 Springer-Verlag, pp. 469–490.

    Google Scholar 

  5. Cruz-Hernández, C. and Nijmeijer, H. (2000) “Synchronization through filtering,” Int. J. Bifurc. Chaos 10(4), 763–775.

    Article  Google Scholar 

  6. Cruz-Hernández, C., Posadas-Castillo C., and Sira-Ramírez, H. (2002) “Synchronization of two hyperchaotic Chua circuits: A generalized Hamiltonian systems approach,” Procs. of 15th IFAC World Congress, July 21–26, Barcelona, Spain.

    Google Scholar 

  7. Cruz-Hernández C. (2004) “Synchronization of time delay Chua's oscillator with application to secure communication,” Nonlinear Dynamics and Systems Theory 4(1), 1–13

    MATH  Google Scholar 

  8. Cuomo, K.M., Oppenheim, A.V. and Strogratz, S.H. (1993) “Synchronization of Lorenz-based chaotic circuits with applications to communications,” IEEE Trans. Circuits Syst. II 40(10), 626–633.

    Article  Google Scholar 

  9. Dedieu, H., Kennedy, M.P., and Hasler, M. (1993) “Chaotic shift keying: Modulation and demodulation of a chaotic carrier using self-synchronizing Chua's circuits,” IEEE Trans. Circuits Syst. II 40(10), 634–642.

    Article  Google Scholar 

  10. Fradkov, A.L., and Pogromsky, A. Yu. (1998) Introduction to control of oscillations and chaos, World Scientific Publishing, Singapore.

    MATH  Google Scholar 

  11. López-Mancilla, D. and Cruz-Hernández, C. (2004) “An anlysis of robustness on the synchronization of chaotic systems under nonvanishing perturbations using sliding modes,” WSEAS Trans. Math. 3(2), 364–269.

    Google Scholar 

  12. López-Mancilla, D. and Cruz-Hernández, C. (2005a) “Output synchronization of chaotic systems: model-matching approach with application to secure communication,” Nonlinear Dynamics and Systems Theory. 5(2), 141–156.

    MATH  Google Scholar 

  13. López-Mancilla, D. and Cruz-Hernández, C. (2005b) “Output synchronization of chaotic oscillators and private communication,” Procs. of 16th IFAC World Congress, July 3–8, Prague, Czech Republic.

    Google Scholar 

  14. López-Mancilla, D. and Cruz-Hernández, C. (2005c) “A note on chaos-based communication schemes,” Revista Mexicana de Física 51(3), 265–269.

    Google Scholar 

  15. Lu, H., He, Y., and He, Z. (1998) “A chaos generator: Analysis of complex dynamics of a cell equation in delayed cellular neural networks,” IEEE Trans. Circuits Syst. 45, 178–181.

    Article  Google Scholar 

  16. Milanovic, V. and Zaghloul, M.E. (1996) “Improved masking algorithm for chaotic communication systems,” Electronics Lett. 32(1), 11–12.

    Article  Google Scholar 

  17. Nijmeijer, H. and Mareels, I.M.Y. (1997) “An observer looks at synchronization,” IEEE Trans. Circuits Syst. I 44(10), 882–890.

    Article  Google Scholar 

  18. Orzo, L., Vidnyanszky, Z., Hamori, J., and Roska, T. (1996) “CNN model of the feature-linked synchronized activities in the visual thalamo-cortical systems,” Proc. 1996 Fourth IEEE Int. Workshop on Cellular Neural Networks and Their Applications (CNNA-96), Seville, Spain, 24–26 June, pp. 291–296.

    Google Scholar 

  19. Parlitz, U., Chua, L.O., Kocarev, Lj., Halle, K.S., and Shang, A. (1992) “Transmission of digital signals by chaotic synchronization,” Int. J. Bifurc. Chaos 2(4), 973–977.

    Article  MATH  Google Scholar 

  20. Pecora, L.M. and Carroll, T.L. (1990) “Synchronization in chaotic systems,” Phys. Rev. Lett. 64, 821–824.

    Article  Google Scholar 

  21. Pikovsky, A., Rosenblum, M., and Kurths, J. (2001) Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge University Press.

    Google Scholar 

  22. Sira-Ramírez, H. and Cruz-Hernández, C. (2001) “Synchronization of Chaotic Systems: A Generalized Hamiltonian Systems Approach,” Int. J. Bifurc. Chaos 11(5), 1381–1395. And in Procs. of American Control Conference (ACC′2000), Chicago, USA, pp. 769–773.

    Article  Google Scholar 

  23. Special Issue (1992) on “Cellular neural networks,” Int. J. Circuit Theor. Appl. 20.

    Google Scholar 

  24. Special Issue (1993) on “Cellular neural networks,” IEEE Trans. Circuits Syst. I and II, 40 (in 2 separate issues).

    Google Scholar 

  25. Special Issue (1995) on “Nonlinear waves, patters, and spatio-temporal chaos,” IEEE Trans. Circuits Syst. I, 42 (in 2 separate issues).

    Google Scholar 

  26. Special Issue (1997 Part I) on “Visions of nonlinear science in the 21st century,” Int. J. Bifurc. Chaos, 7(9–10).

    Google Scholar 

  27. Special Issue (1997a) on “Chaos synchronization and control: Theory and applications,” IEEE Trans. Circuits Syst. I, 44(10).

    Google Scholar 

  28. Special Issue (1997b) on “Control of chaos and synchronization,” Syst. Contr. Lett. 31.

    Google Scholar 

  29. Special Issue (2000) on “Control and synchronization of chaos,” Int. J. Bifurc. Chaos, 10(3–4).

    Google Scholar 

  30. Werblin, F., Roska, T., and Chua, L.O. (1994) “The analogic cellular neural network as a bionic eye,” Int. J. Circuit Theor. Appl. 23, 541–569.

    Article  Google Scholar 

  31. Yang, T. and Chua, L.O. (1996) “Secure communication via chaotic parameter modulation,” IEEE Trans. Circuits Syst. I 43(9), 817–819.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Engineering Faculty, Baja California Autonomous University (UABC) and FIME University Autonomous of Nuevo León (UANL), México

    C. Posadas-Castillo

  2. Telmatics Direction, Scientific Research and Advanced Studies of Ensenada (CICESE), Km. 107 Carretera Tijuana-Ensenada, Ensenada, B.C., 22860, México

    C. Cruz-Hernández

  3. Engineering Faculty, Baja California Autonomous University (UABC), México

    D. López-Mancilla

Authors
  1. C. Posadas-Castillo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Cruz-Hernández
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. López-Mancilla
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Tijuana Institute of Technology, Tijuana, Mexico

    Oscar Castillo

  2. Department of Computer Science, Tijuana Institute of Technology, 4207, Chula Vista, CA, 91909, USA

    Patricia Melin

  3. Polish Academy of Sciences, Systems Research Institute, Newelska 6, Warszawa, 01-447, Poland

    Janusz Kacprzyk

  4. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, T6J 2V4, Canada

    Witold Pedrycz

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer

About this chapter

Cite this chapter

Posadas-Castillo, C., Cruz-Hernández, C., López-Mancilla, D. (2007). Synchronization of Chaotic Neural Networks: A Generalized Hamiltonian Systems Approach. In: Castillo, O., Melin, P., Kacprzyk, J., Pedrycz, W. (eds) Hybrid Intelligent Systems. Studies in Fuzziness and Soft Computing, vol 208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-37421-3_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-37421-3_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37419-0

  • Online ISBN: 978-3-540-37421-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation