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Emergent Dynamical Properties of the BCM Learning Rule

Udeigwe, LC and Munro, PW and Ermentrout, GB (2017) Emergent Dynamical Properties of the BCM Learning Rule. Journal of Mathematical Neuroscience, 7 (1).

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The Bienenstock–Cooper–Munro (BCM) learning rule provides a simple setup for synaptic modification that combines a Hebbian product rule with a homeostatic mechanism that keeps the weights bounded. The homeostatic part of the learning rule depends on the time average of the post-synaptic activity and provides a sliding threshold that distinguishes between increasing or decreasing weights. There are, thus, two essential time scales in the BCM rule: a homeostatic time scale, and a synaptic modification time scale. When the dynamics of the stimulus is rapid enough, it is possible to reduce the BCM rule to a simple averaged set of differential equations. In previous analyses of this model, the time scale of the sliding threshold is usually faster than that of the synaptic modification. In this paper, we study the dynamical properties of these averaged equations when the homeostatic time scale is close to the synaptic modification time scale. We show that instabilities arise leading to oscillations and in some cases chaos and other complex dynamics. We consider three cases: one neuron with two weights and two stimuli, one neuron with two weights and three stimuli, and finally a weakly interacting network of neurons.


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Item Type: Article
Status: Published
CreatorsEmailPitt UsernameORCID
Udeigwe, LC
Munro, PWpwm@pitt.eduPWM
Ermentrout, GB
Date: 1 December 2017
Date Type: Publication
Journal or Publication Title: Journal of Mathematical Neuroscience
Volume: 7
Number: 1
DOI or Unique Handle: 10.1186/s13408-017-0044-6
Schools and Programs: School of Information Sciences > Telecommunications
Refereed: Yes
PubMed ID: 28220467
Date Deposited: 30 Jun 2017 15:06
Last Modified: 30 Mar 2021 10:55


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