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: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/430963 |
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| _version_ | 1832566388831551488 |
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| author | Fangyan Yang Song Tang Guilan Xu |
| author_facet | Fangyan Yang Song Tang Guilan Xu |
| author_sort | Fangyan Yang |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-14587031bb474a6dbfa878acd7eff663 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-14587031bb474a6dbfa878acd7eff6632025-02-03T01:04:18ZengWileyDiscrete 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 |
| spellingShingle | Fangyan Yang Song Tang Guilan Xu Horseshoe Chaos in a 3D Neural Network with Different Activation Functions Discrete Dynamics in Nature and Society |
| title | 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_short | Horseshoe Chaos in a 3D Neural Network with Different Activation Functions |
| title_sort | horseshoe chaos in a 3d neural network with different activation functions |
| url | http://dx.doi.org/10.1155/2013/430963 |
| work_keys_str_mv | AT fangyanyang horseshoechaosina3dneuralnetworkwithdifferentactivationfunctions AT songtang horseshoechaosina3dneuralnetworkwithdifferentactivationfunctions AT guilanxu horseshoechaosina3dneuralnetworkwithdifferentactivationfunctions |