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

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.


  1. Wilson H, Cowan J: Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons. Biophys J. 1972, 12: 1-22.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  2. Gillespie D: Exact stochastic simulation of coupled chemical reactions. J Phys Chem. 1977, 2340-2361. 81

  3. Benayoun M, Cowan J, van Drongelen W, Wallace E: Avalanches in a Stochastic Model of Spiking Neurons. PLoS Comput Biol. 2010, 6: e1000846-10.1371/journal.pcbi.1000846.

    Article  PubMed Central  PubMed  Google Scholar 

  4. Vogels T, Sprekeler H, Zenke F, Clopath C, Gerstner W: Inhibitory Plasticity Balances Excitation and Inhibition in Sensory Pathways and Memory Networks. Science. 2011, 664-666. 334

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

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Correspondence to Jeremy Neuman.

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Neuman, J., Kiewiet, B., Cowan, J.D. et al. Observations of dynamical behavior in a stochastic Wilson-Cowan population with plasticity. BMC Neurosci 14 (Suppl 1), P400 (2013).

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