Skip to main content
SpringerLink
Log in
Book cover

International Symposium on Neural Networks

ISNN 2011: Advances in Neural Networks – ISNN 2011 pp 42–51Cite as

Study on the Synchrony Intensity Threshold of Two Uncoupled Neurons under Different Currents’ Stimulation

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6675))

Abstract

The input current of two uncoupled Hindmarsh-Rose neurons under different initial conditions is modulated by the different membrane potential of the Hindmarsh-Rose neuron; and the synchrony intensity threshold of two uncoupled neurons under different currents’ stimulation by calculating and analyzing their maximum absolute phase difference.Under different simulation signals, the two uncoupled neurons can realize the phase synchronization or the full synchronization, and the stimulation intensity threshold of the two uncoupled neurons’ realizing synchronization is different. According to the signal’s complexity, the more complex the stimulation signal is, the smaller its intensity threshold to realize the two uncoupled neurons’ synchronization is. Under the chaos signal’s stimulation, its intensity threshold to realize the two uncoupled neurons’ synchronization is smaller than the period signal, and is easier than the period signal to realize the two uncoupled neurons’ synchronization. So the chaos discharge paterns is more favourable to signals’ expression and transmission in neural system. From the calcium ion’s effect, the smaller the stimulation neuron’s parameter r is, the smaller the effect of the stimulation signal’s calcium ion is, the easier the two uncoupled neurons realize synchronization. So the stimulation signal whose calcium ion’s effect is large isn’t easy to realize the two uncouple neurons’ synchronization. This investigation shows the synchrony intensity threshold’s rule of two uncoupled neurons under different currents’ stimulation. These results are helpful to study synchronization and encode of many neurons or neural network.

This is a preview of subscription content, 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   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

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. Physical Review Letter 64, 821–824 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  2. Pecora, L.M., Carroll, T.L.: Driving Systems with Chaotic Signals. Physical Review: A 44, 2374–2383 (1991)

    Article  Google Scholar 

  3. Gray, C.M., et al.: Oscillatory Response in Cat Visual Cortex Exhibit Inter-columnar Synchronization Which Reflects Global Stimulus Properties. Nature 338, 334–337 (1989)

    Article  Google Scholar 

  4. Neiman, A.B., Russell, D.F.: Synchronization of Noise-induced Bursts in Noncoupled Sensory Neurons. Phys. Rev. Lett. 88, 138103-1–138103-4 (2002)

    Article  Google Scholar 

  5. Daihai, H., Pengliang, S., Stone, L.: Noise-induced Synchronization in Realistic Models. Physical Review: E 67, 0272011–0272013 (2002)

    Google Scholar 

  6. Yoshida, K., Sato, K., Sugamata, A.: Noise-induced Synchronization of Uncoupled Nonlinear Systems. Journal of Sound and Vibration 290, 34–47 (2006)

    Article  Google Scholar 

  7. Xia, S., Qi-Shao, L.: Coherence Resonance and Synchronization of Hindmarsh-Rose Neurons with Noise. Chinese Physics 14, 1088–1094 (2005)

    Article  Google Scholar 

  8. Wu, Y., Xu, J.-X., Jin, W.-Y., Hong, L.: Detection of Mechanism of Noise-induced Synchronization between Two Identical Uncoupled Neurons. Chin. Phys. Lett. 24, 3066–3069 (2007)

    Article  Google Scholar 

  9. Wu, Y., Xu, J., He, D., Earn, D.J.D.: Generalized Synchronization Induced by Noise and Parameter Mismatching in Hindmarsh-Rose Neurons. Chaos, Solitons and Fractals 23, 1605–1611 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Wu, Y., Xu, J., He, D., Jin, W.: Study on Nonlinear Characteristic of Two Synchronizing Uncoupled Hindmarsh-Rose Neurons. Acta Physica Sinica 54, 3457–3464 (2005)

    Google Scholar 

  11. Wu, C., Xu, J., Jin, W.: Complete Synchronization and Phase Synchronization of Two Uncoupled Neurons through Parametrical drive. Journal of Xi’an Jiaotong University 39, 544–547 (2005)

    Google Scholar 

  12. Wu, Y., Xu, J.-X., He, D., Jin, W., He, M.: Synchronization in Two Uncoupled Chaotic Neurons. In: Yin, F.-L., Wang, J., Guo, C. (eds.) ISNN 2004. LNCS, vol. 3173, pp. 138–143. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Hindmarsh, J.L., Rose, R.M.: A Model of the Nerve Impulse Using Two First-order Differential Equation. Nature 296, 162–165 (1982)

    Article  Google Scholar 

  14. Hindmarsh, J.L., Rose, R.M.: A Model of Neuronal Bursting Using Three Coupled First Order Differential Equations. Series B, Biological Sciences 221, 87–102 (1984)

    Article  Google Scholar 

  15. Peng, Y., Jian, Z., Wang, J.: Study on Discharge Patterns of Hindmarsh-Rose Neurons Under Slow Wave Current Stimulation. In: Jiao, L., Wang, L., Gao, X.-b., Liu, J., Wu, F. (eds.) ICNC 2006. LNCS, vol. 4221, pp. 127–134. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  16. Huerta, R., Rabinovich, M.I.: Spike-train Bifurcation in Two Coupled Chaotic Neurons. Physical Review: E 55, R2108–R2110 (1997)

    Google Scholar 

  17. Ying, W., et al.: Study on Nonlinear Characteristic of Two Synchronizing Uncoupled Hindmarsh-Rose neurons. Physics Letters: A 54, 3457–3464 (2005)

    Google Scholar 

  18. Shuai, J.-W., Durand, D.M.: Phase Synchronization in Two Coupled Chaotic Neurons. Physics Letters: A 264, 289–296 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  19. Peng, Y., et al.: Synchrony of Two Uncoupled Neurons under Half Wave Sine Current Stimulation. Communications in Nonlinear Science and Numerical Simulation 14, 1570–1575 (2009)

    Article  Google Scholar 

  20. Peng, Y., Wang, J.: Study on Synchrony of Two Uncoupled Neurons under the Neuron’s Membrane Potential Stimulation. The Journal of Biomedical Science and Engineering 3, 160–166 (2010)

    Article  Google Scholar 

  21. Peng, Y., Wang, J.: Synchrony of Two Uncoupled Neurons under the Chaos Signal Stimulation. In: The 2nd International Conference on Computer Modeling and Simulation, pp. 355–359 (2009)

    Google Scholar 

  22. Peng, Y., Wang, J.: Study on Synchrony of Two Uncoupled Neurons under Slow Ramp Current Stimulation. In: 2009 Fifth International Conference on Natural Computation, pp. 418–422 (2009)

    Google Scholar 

  23. Peng, Y., Wang, J.: Discharge Patterns’ Change of Hindmarsh-Rose Neurons under Slow Ramp Current Stimulation. In: 2007 2nd International Conference on Bio-Inspired Computing: Theories and Applications, pp. 52–55 (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Communication Engineering Department, Engineering College of Armed Police Force, 710086, Xi’an, China

    Yueping Peng

Authors
  1. Yueping Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Automation, Key Laboratory of Complex Systems and Intelligence Science, Chinese Academy of Sciences, 100190, Beijing, China

    Derong Liu

  2. College of Information Science and Engineering, Shenyang, Northeastern University, 110004, Liaoing, China

    Huaguang Zhang

  3. Department of Electrical and Computer Engineering, University of Cyprus, 75 Kallipoleos Avenue, 1678, Nicosia, Cyprus

    Marios Polycarpou

  4. Dipartimento di Elettronica, Politecnico di Milano, Piazza L. da Vinci 32, 20133, Milano, Italy

    Cesare Alippi

  5. Deptartment of Electrical, Computer and Biomedical Engineering, University of Rhode Island, RI 02881, Kingston, USA

    Haibo He

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Peng, Y. (2011). Study on the Synchrony Intensity Threshold of Two Uncoupled Neurons under Different Currents’ Stimulation. In: Liu, D., Zhang, H., Polycarpou, M., Alippi, C., He, H. (eds) Advances in Neural Networks – ISNN 2011. ISNN 2011. Lecture Notes in Computer Science, vol 6675. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21105-8_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21105-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21104-1

  • Online ISBN: 978-3-642-21105-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation