The Effect of Inhibitory Neurons on a Class of Neural Networks

Márton Neogrády-Kiss () and Péter L. Simon
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Márton Neogrády-Kiss: Eötvös Loránd University Budapest, Institute of Mathematics
Péter L. Simon: Eötvös Loránd University Budapest, Institute of Mathematics

A chapter in Trends in Biomathematics: Modeling Cells, Flows, Epidemics, and the Environment, 2020, pp 97-109 from Springer

Abstract: Abstract The understanding of the effect of inhibitory neurons on neural networks’ dynamics is crucial to gain more insight into the biological process. Here we examine the dynamics of a special excitatory-inhibitory neural network where the network is complete. In this special case the dynamics has an order preserving property if the activation function is a positive bounded monotone increasing function. With a special choice of activation functions such as step functions we are able to analyse the whole dynamics. We do this in the case of two- and three-valued step functions. The three-valued case can exhibit stable limit cycles, so it would be worthwhile to analyse the dynamics on more complicated networks.

Keywords: Step activation function; Hopfield model; Stability; Oscillation (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-46306-9_7

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DOI: 10.1007/978-3-030-46306-9_7

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