Skip to main content

New Chaos Produced from Synchronization of Chaotic Neural Networks

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5263))

Abstract

In this paper, we investigates synchronization dynamics of neural networks. Generalized linear synchronization (GLS) is proposed to acquire a general kind of proportional relationships between two-neuron networks. Under the point of synchronization, we can find that the node has complex dynamics with some interesting characteristics, and some new chaos phenomenons can been found. Numerical simulations show that this method works very well of two-neuron networks with identical Lorenz systems. Also our method can be applied to other systems.

This work was jointly supported by the Doctoral Found of QUST, and the Natural Science Foundation of Henan Province, China under Grant 0611055100.

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

Buying options

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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990)

    Article  MathSciNet  Google Scholar 

  2. Lu, W.L., Chen, T.P.: Synchronization of coupled connected neural networks with delays. IEEE Trans. Circuits and System 51, 2491–2503 (2004)

    Article  MathSciNet  Google Scholar 

  3. Lu, J., Cao, J.: Synchronization-based approach for parameters identification in delayed chaotic neural networks. Physica A 382, 672–682 (2007)

    Article  Google Scholar 

  4. Yu, W., Cao, J., Lv, J.: Global synchronization of linearly hybrid coupled networks with time-varying delay. SIAM Journal on Applied Dynamical Systems 7, 108–133 (2008)

    Article  MathSciNet  Google Scholar 

  5. Cao, J., Wang, Z., Sun, Y.: Synchronization in an array of linearly stochastically coupled networks with time delays. Physica A 385, 718–728 (2007)

    Article  Google Scholar 

  6. Sun, Y., Cao, J.: Adaptive synchronization between two different noise-perturbed chaotic systems with fully unknown parameters. Physica A 376, 253–265 (2007)

    Article  MathSciNet  Google Scholar 

  7. Sun, Y., Cao, J.: Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation. Physics Letters A 364, 277–285 (2007)

    Article  Google Scholar 

  8. Yu, W., Cao, J.: Adaptive Q-S (lag, anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks. Chaos 16, 023119 (2006)

    Article  MathSciNet  Google Scholar 

  9. Cao, J., Lu, J.: Adaptive synchronization of neural networks with or without time-varying delays. Chaos 16, 013133 (2006)

    Article  MathSciNet  Google Scholar 

  10. Cao, J., Lu, J.: Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters. Chaos 15, 043901 (2005)

    Article  MathSciNet  Google Scholar 

  11. Amritkar, R.E.: Spatially synchronous extinction of species under external forcing. Phys. Rev. Lett. 96, 258102 (2006)

    Article  Google Scholar 

  12. Shahverdiev, E.M., Sivaprakasam, S., Shore, K.A.: Lag synchronization in time-delayed systems. Physics Letters A 292, 320–324 (2002)

    Article  MATH  Google Scholar 

  13. Li, C., Yan, J.: Generalized projective synchronization of chaos: The cascade synchronization approach. Chaos, Solitons and Fractals 30, 140–146 (2006)

    Article  MathSciNet  Google Scholar 

  14. Li, G.: Generalized projective synchronization of two chaotic systems by using active control. Chaos, Solitons and Fractals 30, 77–82 (2006)

    Article  MATH  Google Scholar 

  15. Kittel, A., Parisi, J., Pyragas, K.: Generalized synchronization of chaos in electronic circuit experiments. Physica D 112, 459–471 (1998)

    Article  MATH  Google Scholar 

  16. Li, G.: Modified projective synchronization of chaotic system. Chaos, Solitons and Fractals 32, 1786–1790 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  17. Ronnie, M., Jan, R.: Projective synchronization in three-dimensional chaotic systems. Phys. Rev. Lett. 82, 3042–3045 (1999)

    Article  Google Scholar 

  18. Xu, D., Li, Z.: Controlled projective synchronization in nonpartially-linear chaotic systems. Int. J. Bifurcat Chaos 12, 1395–1402 (2002)

    Article  Google Scholar 

  19. Xu, D., Chee, C., Li, C.: A necessary condition of projective synchronization in discrete-time systems of arbitrary dimensions. Chaos, Solitons and Fractals 22, 175–180 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  20. Rulkov, N.F., Sushchik, M.M., Tsimring, L.S., et al.: Generalized synchronization of chaos in directionally coupled chaotic systems. Phys. Rev. E 51, 980–994 (1995)

    Article  Google Scholar 

  21. Kittel, A., Parisi, J., Pyragas, K.: Generalized synchronization of chaos in electronic circuit experiments. Physica D 112, 459–471 (1998)

    Article  MATH  Google Scholar 

  22. Kocarev, L., Parlitz, U.: Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. Phys. Rev. Lett. 76, 1816–1819 (1996)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cheng, Z. (2008). New Chaos Produced from Synchronization of Chaotic Neural Networks. In: Sun, F., Zhang, J., Tan, Y., Cao, J., Yu, W. (eds) Advances in Neural Networks - ISNN 2008. ISNN 2008. Lecture Notes in Computer Science, vol 5263. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87732-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-87732-5_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87731-8

  • Online ISBN: 978-3-540-87732-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics