Phase Coding on the Large-Scaled Neuronal Population Subjected to Stimulation

  • Rubin Wang
  • Xianfa Jiao
  • Jianhua Peng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4221)


A stochastic nonlinear model of neuronal activity in a neuronal population is proposed in this paper, where the combined dynamics of phase and amplitude is taken into account. An average number density is introduced to describe collective behavior of neuronal population, and a firing density of neurons in the neuronal population is referred to be neural coding. The numerical simulations show that with a weaker stimulation, the response of the neuronal population to stimulation grows up gradually, the coupling configuration among neurons dominates the evolution of the average number density, and new neural coding emerges. Whereas, with a stronger stimulation, the neuronal population responds to the stimulation rapidly, the stimulation dominates the evolution of the average number density, and changes the coupling configuration in the neuronal population.


Neuronal Population Firing Pattern Neural Code Phase Code Strong Stimulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gray, C.M., Konig, P., Engle, A.K., Singer, W.: Oscillatory Responses in Cat Visual Cortex Exhibit Intercolumnar Synchronization Which Reflects Global Stimulus Properties. Nature 338, 334–337 (1989)CrossRefGoogle Scholar
  2. 2.
    Eckhorn, R., Bauer, R., Jordon, W., Brosch, M., Kruse, W., Munk, M., Reitboeck, H.J.: Coherent Oscillations: A Mechanism of Feature Linking in the Visual Cortex? Multiple Electrode and Correlation Analyses in the Cat. Biol. Cybern. 60, 121 (1988)CrossRefGoogle Scholar
  3. 3.
    Winfree, A.T.: The Geometry of Biological Time. Springer, New York (1980)MATHGoogle Scholar
  4. 4.
    Kuramoto, Y.: Chemical Oscillations, Waves, and Turbulence. Springer, Berlin (1984)MATHGoogle Scholar
  5. 5.
    Strogatz, S.H., Marcus, C.M., Westervelt, R.M., Mirollo, R.E.: Simple Model of Collective Transport with Phase Slippage. Phys. Rev. Lett. 61, 2380–2383 (1988)CrossRefGoogle Scholar
  6. 6.
    Tass, P.A.: Phase resetting in Medicine and Biology. Springer, Berlin (1999)MATHGoogle Scholar
  7. 7.
    Colicos, M.A., Collins, B.E., Sailor, M.J., Goda, Y.: Remodeling of Synaptic Actin Induced by Photoconductive Stimulation. Cell 107, 605–616 (2001)CrossRefGoogle Scholar
  8. 8.
    Gazzaniga, M.S., Lvry, R.B., Mangum, G.R.: Cognitive Neuroscience. The Biology of the Mind, 2nd edn. W.W. Norton & Company, New York, London (2002)Google Scholar
  9. 9.
    Han, T.Z., Wu, F.M.: Neurobiology of Learning and Memory. Beijing Medical University Publisher, Beijing (1998)Google Scholar
  10. 10.
    Wang, R., Yu, W.: A Stochastic Nonlinear Evolution Model and Dynamic Neural Coding on Spontaneous Behavior of Large-Scale Neuronal Population. Advances in Natural Computation Part 1, 490–497 (2005)CrossRefGoogle Scholar
  11. 11.
    Wang, R., Zhang, Z.: Nonlinear Stochastic Models of Neurons Activities. Neurocomputing 51C, 401–411 (2003)CrossRefGoogle Scholar
  12. 12.
    Wang, R., Hayashi, H., Zhang, Z.: A Stochastic Nonlinear Evolution Model of Neuronal Activity with Random Amplitude. In: Proceedings of 9th International Conference on Neural information Processing, vol. 5, pp. 2497–2502 (2002)Google Scholar
  13. 13.
    Wang, R., Chen, H.: A Dynamic Evolution Model for the Set of Populations of Neurons. Int. J. Nonlinear Sci. Numer..Simul. 4, 203–208 (2003)Google Scholar
  14. 14.
    Jiao, X., Wang, R.: Nonlinear Dynamic Model and Neural Coding of Neuronal Network with the Variable Coupling Strength in the Presence of External Stimuli. Applied Physics Letters 87, 083901-3 (2005)Google Scholar
  15. 15.
    Wang, R., Jiao, X.: Stochastic Model and Neural Coding of Large-Scale Neuronal Population with Variable Coupling Strength. Neurocomputing 69, 778–785 (2006)CrossRefGoogle Scholar
  16. 16.
    Wang, R., Jiao, X., Yu, W.: Some Advance in Nonlinear Stochastic Evolution Models for Phase Resetting Dynamics on Populations of Neuronal Oscillators. Int. J. Nonlinear Sci. Numer.Simul. 4, 435–446 (2003)Google Scholar
  17. 17.
    Wang, R., Hayashi, H.: An Exploration of Dynamics of the Moving Mechanism of the Growth Cone. Molecules 8, 127–138 (2003)CrossRefGoogle Scholar
  18. 18.
    Jiao, X., Wang, R.: Nonlinear Stochastic Evolution Model of Variable Coupled Neuronal Oscillator Population in the Presence of External Stimuli. Control and Decision 20, 897–900 (2005)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Rubin Wang
    • 1
    • 2
  • Xianfa Jiao
    • 2
    • 3
  • Jianhua Peng
    • 1
  1. 1.Institute for Brain Information Processing and Cognitive Neurodynamics, School of Information Science and EngineeringEast China University of Science and TechnologyShanghaiChina
  2. 2.College of Information Science and TechnologyDonghua UniversityShanghaiChina
  3. 3.School of ScienceHefei University of TechnologyHe feiChina

Personalised recommendations