Biological Cybernetics

, Volume 101, Issue 1, pp 43–47 | Cite as

Activity patterns in networks stabilized by background oscillations

Original Paper

Abstract

The brain operates in a highly oscillatory environment. We investigate here how such an oscillating background can create stable organized behavior in an array of neuro-oscillators that is not observable in the absence of oscillation, much like oscillating the support point of an inverted pendulum can stabilize its up position, which is unstable without the oscillation. We test this idea in an array of electronic circuits coming from neuroengineering: we show how the frequencies of the background oscillation create a partition of the state space into distinct basins of attraction. Thus, background signals can stabilize persistent activity that is otherwise not observable. This suggests that an image, represented as a stable firing pattern which is triggered by a voltage pulse and is sustained in synchrony or resonance with the background oscillation, can persist as a stable behavior long after the initial stimulus is removed. The background oscillations provide energy for organized behavior in the array, and these behaviors are categorized by the basins of attraction determined by the oscillation frequencies.

Keywords

Neuro-oscillator Categorization Binding Phase-locking 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Buzsaki G (2006) Rhythms of the brain. Oxford University Press, OxfordCrossRefGoogle Scholar
  2. Carrillo H, Hoppensteadt F (2009) Unfolding an electronic integrate-and-fire circuit (submitted)Google Scholar
  3. Feynman R (1965) Lectures in physics. Addison-Wesley, Menlo ParkGoogle Scholar
  4. Guttman R et al (1980) J Membr Physiol 56: 9–18CrossRefGoogle Scholar
  5. Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 1: 500–544Google Scholar
  6. Hoppensteadt FC (2000) Analysis and simulation of chaotic systems. Springer, New YorkGoogle Scholar
  7. Hoppensteadt F (2006) Voltage-controlled oscillations in neurons. Scholarpedia 1(11): 1599Google Scholar
  8. Hoppensteadt FC, Izhikevich EM (1997) Weakly connected neural networks. Springer, New YorkGoogle Scholar
  9. Hoppensteadt FC, Izhikevich EM (1999) Oscillatory neurocomputers with dynamic connectivity. Phys Rev Lett 82: 2983–2986CrossRefGoogle Scholar
  10. Kiehl RA, Yang T, Chua LO (2001) Tunneling-phase logic based cellular nonlinear networks. In: 15th European conference circuit theory and designGoogle Scholar
  11. McAdams ET, Jossinet J (1995) Tissue impedance: a historical overview. Physiol Meas 16: A1–A13PubMedCrossRefGoogle Scholar
  12. Nuñez P (1995) Neocortical dynamics and human EEG rhythms. Oxford University Press, OxfordGoogle Scholar
  13. Singer W (2007) Binding by synchrony. Scholarpedia 2(12): 1657Google Scholar
  14. van der Pol B, van der Mark J (1928) The heartbeat considered as a relaxation oscillation, and an electrical model of the heart. J Sci Ser 7 6: 763–775Google Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

Personalised recommendations