Horseshoe Chaos in a 3D Neural Network with Different Activation Functions

Horseshoe Chaos in a 3D Neural Network with Different Activation Functions

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...

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Main Authors: Fangyan Yang, Song Tang, Guilan Xu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2013/430963
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spelling doaj-14587031bb474a6dbfa878acd7eff6632020-11-25T01:02:12ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/430963430963Horseshoe Chaos in a 3D Neural Network with Different Activation FunctionsFangyan Yang0Song Tang1Guilan Xu2School of Optoelectronic Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaKey Laboratory of Industrial Internet of Things & Networked Control of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaKey Laboratory of Industrial Internet of Things & Networked Control of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaThis 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.http://dx.doi.org/10.1155/2013/430963
collection DOAJ
language English
format Article
sources DOAJ
author Fangyan Yang
Song Tang
Guilan Xu
spellingShingle Fangyan Yang
Song Tang
Guilan Xu
Horseshoe Chaos in a 3D Neural Network with Different Activation Functions
Discrete Dynamics in Nature and Society
author_facet Fangyan Yang
Song Tang
Guilan Xu
author_sort Fangyan Yang
title Horseshoe Chaos in a 3D Neural Network with Different Activation Functions
title_short Horseshoe Chaos in a 3D Neural Network with Different Activation Functions
title_full Horseshoe Chaos in a 3D Neural Network with Different Activation Functions
title_fullStr Horseshoe Chaos in a 3D Neural Network with Different Activation Functions
title_full_unstemmed Horseshoe Chaos in a 3D Neural Network with Different Activation Functions
title_sort horseshoe chaos in a 3d neural network with different activation functions
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2013-01-01
description 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.
url http://dx.doi.org/10.1155/2013/430963
work_keys_str_mv AT fangyanyang horseshoechaosina3dneuralnetworkwithdifferentactivationfunctions
AT songtang horseshoechaosina3dneuralnetworkwithdifferentactivationfunctions
AT guilanxu horseshoechaosina3dneuralnetworkwithdifferentactivationfunctions
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