Stability analysis of associative memory network composed of stochastic neurons and dynamic synapses

Yuichi Katori

doi:10.3389/fncom.2013.00006

Abstract

We investigate the dynamical properties of an associative memory network consisting of stochastic neurons and dynamic synapses that show short-term depression and facilitation. In the stochastic neuron model used in this study, the efficacy of the synaptic transmission changes according to the short-term depression or facilitation mechanism. We derive a macroscopic mean field model that captures the overall dynamical properties of the stochastic model. We analyze the stability and bifurcation structure of the mean field model, and show the dependence of the memory retrieval performance on the noise intensity and parameters that determine the properties of the dynamic synapses, i.e., time constants for depressing and facilitating processes. The associative memory network exhibits a variety of dynamical states, including the memory and pseudo-memory states, as well as oscillatory states among memory patterns. This study provides comprehensive insight into the dynamical properties of the associative memory network with dynamic synapses.

Highlights

Dynamic synapses change their transmission efficacy depending on the activity of the presynaptic neuron, and the postsynaptic response can be decreased or increased (Markram and Tsodyks, 1996; Tsodyks and Markram, 1997; Markram et al, 1998; Thomson, 2000; Wang et al, 2006)
Change in the transmission efficacy is modeled by variables that represent the releasable neurotransmitters and the utilization parameter that defines the fraction of the neurotransmitter release by each action potential, reflecting the calcium concentration
In this study, we investigated the dynamical properties of an associative memory network composed of a stochastic neural network with both short-term depression and facilitation synapses on the basis of the macroscopic mean field model

Summary

Introduction

Dynamic synapses change their transmission efficacy depending on the activity of the presynaptic neuron, and the postsynaptic response can be decreased (short-term depression) or increased (short-term facilitation) (Markram and Tsodyks, 1996; Tsodyks and Markram, 1997; Markram et al, 1998; Thomson, 2000; Wang et al, 2006). Activation of a presynaptic neuron and generation of an action potential causes influx of calcium ions into the presynaptic membrane. A chemical reaction with the calcium ions triggers the release of the neurotransmitters and induces the post synaptic current. If many action potentials are generated in a short period of time, the calcium concentration and the fraction of releasable neurotransmitters change, and the transmission efficacy increases or decreases transiently. Change in the transmission efficacy is modeled by variables that represent the releasable neurotransmitters and the utilization parameter that defines the fraction of the neurotransmitter release by each action potential, reflecting the calcium concentration

Methods

Results

Conclusion