Skip to main content

Global Synchronization of Ghostburster Neurons Via Active Control

  • Conference paper
Bio-Inspired Computational Intelligence and Applications (LSMS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4688))

Included in the following conference series:

  • 1375 Accesses

Abstract

In this paper, active control law is derived and applied to control and synchronize two unidirectional coupled Ghostbursters neurons under external electrical stimulation. Firstly, the dynamical behavior of the nonlinear Ghostburster model responding to various external electrical stimulations is studied. Then, using the results of the analysis, the active control strategy is designed for global synchronization of the two unidirectional coupled neurons and stabilizing the chaotic bursting trajectory of the slave system to desired tonic firing of the master system. Numerical simulations demonstrate the validity and feasibility of the proposed method.

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. Caroll, T.L., Pecora, L.M.: Synchronizing chaotic circuits. IEEE Trans. Circ. Syst. I 38, 453–456 (1991)

    Article  Google Scholar 

  2. Liao, T.L.: Adaptive synchronization of two Lorenz systems. Chaos, Solitons & Fractals 9, 1555–1561 (1998)

    Article  MATH  Google Scholar 

  3. Restrepo, J.G., Ott, E., Hunt, B.R.: Emergence of synchronization in complex networks of interacting dynamical systems. Physics D: Nonlinear Phenomena 224, 114–122 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  4. Yang, J.Z., Hu, G.: Three types of generalized synchronization. Physics Letters A 361, 332–335 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. David, I., Almeida, R., Alvarez, J., Barajas, J.G.: Robust synchronization of Sprott circuits using sliding mode control. Chaos, Solitons & Fractals 30 (2006)

    Google Scholar 

  6. Cuomo, K.M., Oppenheim, A.V., Strogatz, S.H.: Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Trans. Circ. Syst. I 40, 626–633 (1993)

    Article  Google Scholar 

  7. Meister, M., Wong, R.O., Baylor, D.A., Shatz, C.J.: Synchronous bursts of action potentials in ganglion cells of the developing mammalian retina. Science 252, 939–943 (1991)

    Article  Google Scholar 

  8. Kreiter, A.K., Singer, W.: Stimulus-dependent synchronization of neuronal responses in the visual cortex of the awake macaque monkey. J. Neurons 16, 2381–2396 (1996)

    Google Scholar 

  9. Garbo, A.D., Barbi, M., Chillemi, S.: The synchronization properties of a network of inhibitory interneurons depend on the biophysical model. BioSystems 88, 216–227 (2007)

    Article  Google Scholar 

  10. Elson, R.C., Selverston, A.I., Huerta, R., Rulkov, N.F., Rabinovich, M.I., Abarbanel, H.D.I.: Synchronization behavior of two coupled biological Neurons. Physical Review Letters 81, 5692–5695 (1999)

    Article  Google Scholar 

  11. Gray, C.M., Konig, P., Engel, A.K., Singer, W.: Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature 338, 334–337 (1989)

    Article  Google Scholar 

  12. Yu, H., Peng, J.: Chaotic synchronization and control in nonlinear-coupled Hindmarsh–Rose neural systems. Chaos, Solitons & Fractals 29, 342–348 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. David, I., Almeida, R., Alvarez, J., Barajas, J.G.: Robust synchronization of Sprott circuits using sliding mode control. Chaos, Solitons & Fractals 30, 11–18 (2006)

    Article  MATH  Google Scholar 

  14. Longtin, A.: Effect of noise on the tuning properties of excitable systems. Chaos, Solitons & Fractals 11, 1835–1848 (2000)

    Article  MATH  Google Scholar 

  15. Doiron, B., Laing, C., Longtin, A.: Ghostbursting: A Novel Neuronal Burst Mechanism. Journal of Computational Neuroscience 12, 5–25 (2002)

    Article  Google Scholar 

  16. Laing, C.R., Doiron, B., Longtin, A., Maler, L.: Ghostburster: the effects of dendrites on spike patterns. Neurocomputing 44, 127–132 (2002)

    Article  Google Scholar 

  17. Liao, X.X., Chen, G.R.: Chaos synchronization of general Lur’e systems via time-delay feedback control. Int. J. Bifurcat Chaos 13, 207–213 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  18. Bowong, S., Kakmeni, F.M.M.: Synchronization of uncertain chaotic systems via backstepping approach. Chaos, Solitons & Fractals 21, 999–1011 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  19. Wang, C., Ge, S.S.: Adaptive synchronization of uncertain chaotic systems via backstepping design. Chaos, Solitons & Fractals 12, 1199–1206 (2001)

    Article  MATH  Google Scholar 

  20. Wang, L.X.: Adaptive Fuzzy System and Control: Design and Stability Analysis. Prentice-Hall, Englewood Cliffs (1994)

    Google Scholar 

  21. Bai, E.W., Lonngran, E.E.: Synchronization of two Lorenz systems using active control. Chaos, Solitons & Fractals 8, 51–58 (1997)

    Article  MATH  Google Scholar 

  22. Wang, C.C., Su, J.P.: A new adaptive variable structure control for chaotic synchronization and secure communication. Chaos, Solitons & Fractals 20(5), 967–977 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  23. Bai, E., Lonngrn, K.E.: Sequential synchronization of two Lorenz systems using active control. Chaos, Solitons & Fractals 11, 1041–1044 (2000)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Kang Li Minrui Fei George William Irwin Shiwei Ma

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, J., Chen, L., Deng, B., Dong, F. (2007). Global Synchronization of Ghostburster Neurons Via Active Control. In: Li, K., Fei, M., Irwin, G.W., Ma, S. (eds) Bio-Inspired Computational Intelligence and Applications. LSMS 2007. Lecture Notes in Computer Science, vol 4688. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74769-7_64

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-74769-7_64

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74768-0

  • Online ISBN: 978-3-540-74769-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics