Skip to main content

Model Studies on Time-Scaled Phase Response Curves and Synchronization Transition

  • Conference paper
Neural Information Processing. Theory and Algorithms (ICONIP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6443))

Included in the following conference series:

  • 2442 Accesses

Abstract

We studied possibilities of classification of single spike neuron models by their intrinsic timescale parameters, because little is known about changes of timescale on spiking dynamics, and its influence on other spike properties and network dynamics such as synchronization. Using both FitzHugh-Nagumo (FHN) type and Terman-Wang (TW) type of theoretically tractable models, analysis of the phase response curve (PRC) found common and unique dynamic characteristics with respect to two parameters of timescale and injected current amplitude in the models. Also, a scheme of synchronization transition in the identical pair systems, in which two identical models mutually interact through the same model of synaptic response, was systematically explained by controlling these parameters. Then we found their common and unique synchronous behaviors.

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. von der Malsburg, C.: The correlation theory of brain function. Internal Report 81-2, Dept. of Neurobiology, Max-Planck-Institute for Biophysical Chemistry, Göttingen, Germany (1981)

    Google Scholar 

  2. Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117(4), 500–544 (1952)

    Article  Google Scholar 

  3. Morris, C., Lecar, H.: Voltage oscillations in the barnacle giant muscle fiber. Biophys. J. 35(1), 193–213 (1981)

    Article  Google Scholar 

  4. FitzHugh, R.: Mathematical models of excitation and propagation in nerve. In: Schwan, H.P. (ed.) Biological Engineering. ch. 1, pp. 1–85. McGraw-Hill Book Co, N.Y (1969)

    Google Scholar 

  5. Terman, D., Wang, D.L.: Global competition and local cooperation in a network of neural oscillators. Physica D 81, 148–176 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ermentrout, B.: Type I membranes, phase resetting curves and synchrony. Neural Computation 8, 979–1001 (1996)

    Article  Google Scholar 

  7. Gerstner, W., Kistler, W.M.: Spiking Neuron Models. Single Neurons, Populations, Plasticity. Cambridge University Press, New York (2002)

    Book  MATH  Google Scholar 

  8. Kuramoto, Y.: Chemical Oscillations, Waves, and Turbulence. Springer, Tokyo (1984)

    Book  MATH  Google Scholar 

  9. Rall, W.: Distinguishing theoretical synaptic potentials computed for different soma-dendritic distributions of synaptic inputs. J. Neurophysiol. 30, 1138–1168 (1967)

    Google Scholar 

  10. Frankel, P., Kiemel, T.: Relative phase behavior of two slowly coupled oscillators. SIAM J. Appl. Math. 53, 1436–1446 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  11. Sato, Y.D.: Synchronization Phenomena in a Pair of Coupled Neuronal Oscillator Systems. PhD Thesis, Tokyo Institute of Technology (2005)

    Google Scholar 

  12. Van Vreeswijk, C., Abbott, L.F., Ermentrout, G.B.: Inhibition, not excitation, synchronizes coupled neurons. J. Comput. Neurosci. 1, 303–313 (1994)

    Google Scholar 

  13. Van Vreeswijk, C.: Partially synchronized states in networks of pulse-coupled neurons. Phys. Rev. E 54, 5522–5537 (1996)

    Article  Google Scholar 

  14. Mehrotra, A., Sangiovanni-Vincentelli, A.: Noise Analysis of Radio Frequency Circuits. Kluwer Academic Publishers, Dordrecht (2004)

    Book  MATH  Google Scholar 

  15. Sato, Y.D., Shiino, M.: Generalization of coupled spiking models and effects of the width of an action potential on synchronization phenomena. Phys. Rev. E 75, 011909 (2007)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sato, Y.D., Okumura, K., Shiino, M. (2010). Model Studies on Time-Scaled Phase Response Curves and Synchronization Transition. In: Wong, K.W., Mendis, B.S.U., Bouzerdoum, A. (eds) Neural Information Processing. Theory and Algorithms. ICONIP 2010. Lecture Notes in Computer Science, vol 6443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17537-4_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-17537-4_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17536-7

  • Online ISBN: 978-3-642-17537-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics