Horseshoe chaos in a 3D neural network with different activation functions
type: Item
instance of: scholarly article
title: Horseshoe chaos in a 3D neural network with different activation functions
zbMATH Open document ID: 1417.92012
DOI: 10.1155/2013/430963
author: Song Tang
author: Guilan Xu
author: Fangyan Yang
published in: Discrete Dynamics in Nature and Society
publication date: 2013-06-13T00:00:00Z
review text: Summary: This paper studies a small neural network with three neurons. First, the activation function takes the sign function. Although the network is a simple hybrid system with all subsystems being exponentially stable, we find that it can exhibit very complex dynamics such as limit cycles and chaos. Since the sign function is a limit case of sigmoidal functions, we find that chaos robustly exists with some different activation functions, which implies that such chaos in this network is more related to its weight matrix than the type of activation functions. For chaos, we present a rigorous computer-assisted study by virtue of topological horseshoe theory.
Mathematics Subject Classification ID: 92B20
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 37N25
zbMATH DE Number: 6175083
Wikidata QID: Q58921591
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/430963
OpenAlex ID: W1995224169
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description: scientific article; zbMATH DE number 6175083