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

Fangyan Yang | Zendy; Song Tang | Zendy; Guilan Xu | Zendy

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

Author(s) -

Fangyan Yang,

Song Tang,

Guilan Xu

Publication year - 2013

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2013/430963

Subject(s) - activation function , sigmoid function , sign (mathematics) , limit (mathematics) , chaos (operating system) , artificial neural network , computer science , function (biology) , sign function , horseshoe (symbol) , topology (electrical circuits) , mathematics , control theory (sociology) , mathematical analysis , artificial intelligence , control (management) , combinatorics , computer security , evolutionary biology , biology , programming language

This paper studies a small neural network with three neurons. First, the activationfunction takes the sign function. Although the network is a simple hybrid systemwith all subsystems being exponentially stable, we find that it can exhibit verycomplex dynamics such as limit cycles and chaos. Since the sign function is a limitcase of sigmoidal functions, we find that chaos robustly exists with some differentactivation functions, which implies that such chaos in this network is more related to itsweight matrix than the type of activation functions. For chaos, we present a rigorouscomputer-assisted study by virtue of topological horseshoe theory

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