Skip to main content

Chaotic Synchronization of Delayed Neural Networks

  • Conference paper
Advances in Neural Networks – ISNN 2005 (ISNN 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3496))

Included in the following conference series:

  • 975 Accesses

Abstract

In this paper, synchronization issue of a coupled time-delayed neural system with chaos is investigated. A sufficient condition for determining the exponential synchronization between the drive and response systems is derived via Lyapunov-Krasovskii stability theorem. Moreover, the synchronization thresholds of the coupled systems are estimated based on the proposed result. The effectiveness of our scheme is illustrated by numerical simulation.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Kocarev, L., Parlitz, U.: General Approach for Chaotic Synchronization with Applications to Communication. Phys. Rev. Lett. 74, 5028 (1995)

    Article  Google Scholar 

  2. Cuomo, K.M., Oppenheim, A.V., Strogatz, S.H.: Synchronization of Lorenz-based Chaotic Circuits with Applications to Communications. IEEE Trans. Circuits Syst. II 40, 626–633 (1993)

    Article  Google Scholar 

  3. Grassi, G., Mascolo, S.: Prentice-Hall, Englewood Cliffs, NJ (1999)

    Google Scholar 

  4. Yang, T., Chua, L.O.: Secure Communication via Chaotic Parameter Modulation. IEEE Trans. Circuits Syst. I 43, 817–819 (1996)

    Article  Google Scholar 

  5. Pecora, L.M., Carroll, T.L.: Synchronization in Chaotic Systems. Phys. Rev. Lett. 64, 821–824 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  6. Pecora, L.M., Carroll, T.L.: Driving Systems with Chaotic Signals. Phys. Rev. A 44, 2374–2383 (1991)

    Article  Google Scholar 

  7. Thornburg Jr., K.S., Moller, M., Roy, R., Carr, T.W.: Chaos and Coherence in Coupled Lasers. Phys. Rev. E 55, 3865 (1997)

    Article  Google Scholar 

  8. Pasemann, F.: Synchronized Chaos and Other Coherent States for Two Coupled Neurons. Physica D 128, 236–249 (1999)

    Article  MATH  Google Scholar 

  9. Tnonnelier, A., et al.: Synchronization and Desynchronization of Neural Oscillators. Neural Networks 12, 1213–1228 (1999)

    Article  Google Scholar 

  10. Gopalsamy, K., Leung, I.K.C.: Convergence Under Dynamical Thresholds with Delays. IEEE Neural Networks 8, 341–348 (1994)

    Article  Google Scholar 

  11. Liao, X.F., et al.: Hopf Bifurcation and Chaos in a Single Delayed Neuron Equation with Non-monotonic Activation Function. Chaos Solitons Fract 12, 1535–1547 (2001)

    Article  MATH  Google Scholar 

  12. Barsella, A., Lepers, C.: Chaotic Lag Synchronization and Pulse-induced Transient Chaos in Lasers Coupled by Saturable Absorber. Opt. Commun. 205, 397–403 (2002)

    Article  Google Scholar 

  13. Wang, X.J., Rinzel, J.: Alternating and Synchronous Rhythms in Reciprocally Inhibitory Model Neurons. Neural Comput. 4, 84 (1992)

    Article  Google Scholar 

  14. Li, C.D., et al.: Chaotic Lag Synchronization of Coupled Time-delayed Systems and its Applications in Secure Communication. Physica D 194, 187–202 (2004)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tu, F., Liao, X., Li, C. (2005). Chaotic Synchronization of Delayed Neural Networks. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_54

Download citation

  • DOI: https://doi.org/10.1007/11427391_54

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25912-1

  • Online ISBN: 978-3-540-32065-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics