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Journal of Mathematical Biology

, Volume 61, Issue 4, pp 501–526 | Cite as

Uncovering bifurcation patterns in cortical synapses

  • Michael Small
  • Hugh P. C. Robinson
  • Ingo C. Kleppe
  • Chi Kong Tse
Article

Abstract

Individual cortical synapses are known to exhibit a very complex short-time dynamic behaviour in response to simple “naturalistic” stimulation. We describe a computational study of the experimentally obtained excitatory post-synaptic potential trains of individual cortical synapses. By adopting a new nonlinear modelling scheme we construct robust and repeatable models of the underlying dynamics. These models suggest that cortical synapses exhibit a wide range of either periodic or chaotic dynamics. For stimulus at a fixed rate our models predict that the response of the individual synapse will vary from a fixed point to periodic and chaotic, depending on the frequency of stimulus. Dynamics for individual synapses vary widely, suggesting that the individual behaviour of synapses is highly tuned and that the dynamic behaviour of even a small network of synapse-coupled neurons could be extremely varied.

Keywords

Cortical synaptic transmission Bifurcation and chaos Nonlinear time series analysis Modelling 

Mathematics Subject Classification (2000)

37M10 92C20 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Michael Small
    • 1
  • Hugh P. C. Robinson
    • 2
  • Ingo C. Kleppe
    • 2
  • Chi Kong Tse
    • 1
  1. 1.Department of Electronic and Information EngineeringHong Kong Polytechnic UniversityKowloonHong Kong
  2. 2.Department of Physiology, Development and NeuroscienceUniversity of CambridgeCambridgeUK

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