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Observations of dynamical behavior in a stochastic Wilson-Cowan population with plasticity

  • 1Email author,
  • 2,
  • 3 and
  • 4
BMC Neuroscience201314 (Suppl 1) :P400

  • Published:


  • Dynamical Behavior
  • Stochastic Model
  • Brain Activity
  • Synaptic Plasticity
  • Potential Sign

Understanding network connectivity and its role in brain activity is an arduous task. Complicating matters further is the introduction of synaptic plasticity rules. Observations using a mean-field perspective [1] are by their nature incomplete so, here, a stochastic model, which includes fluctuations, has been employed. This analysis shows that two types of network connections, driven by plasticity, exhibit oscillatory behavior signaled by a flipping between Up and Down states. Fluctuations in each state in both setups display power law-like avalanche distributions.

This study, employing a stochastic algorithm [2] used previously in a population-based model [3], introduces plasticity, according to a modified version of [4], into both an E → E and I → E network (Figure 1A). The former network includes plastic excitatory, anti-Hebbian synapses, connecting the populations, while the latter contains plastic inhibitory Hebbian synapses. Both networks incorporate a constant recurrent excitatory synapse. Dynamically, each network undergoes oscillations of relaxation type (Figure 1B) with fluctuations whose avalanche distributions look like power laws (Figure 1C).
Figure 1
Figure 1

Network configuration with two populations. (A) Diagram of the connection. If H is an excitatory population, synapse Wh has anti-Hebbian plasticity. If H represents an inhibitory population, the synapse has Hebbian plasticity. (B) Phase plot of activity of E versus the strength of Wh in the scenario where H is an inhibitory network. (C) The avalanche distribution of the Up state in panel (B).


Understanding the dynamics of plasticity-driven neural networks is vital. Here, it was shown that a stochastic Wilson-Cowan population connected to an exterior population can naturally exhibit relaxation oscillations. This result with its power law avalanche statistics is a potential sign of self-organized criticality.



This work was supported by the Dr. Ralph and Marian Falk Medical Research Trust Fund.

Authors’ Affiliations

Dept. of Physics, University of Chicago, Chicago, IL 60637, USA
Dept. of Applied Mathematics, University of Twente, 7500, AE, Enschede, Netherlands
Dept. of Mathematics, University of Chicago, Chicago, IL 60637, USA
Dept. of Pediatrics, University of Chicago, Chicago, IL 60637, USA


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© Neuman et al; licensee BioMed Central Ltd. 2013

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.