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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 430963, 6 pages
http://dx.doi.org/10.1155/2013/430963
Research Article

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

1School of Optoelectronic Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2Key Laboratory of Industrial Internet of Things & Networked Control of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received 22 February 2013; Accepted 20 March 2013

Academic Editor: Xiao-Song Yang

Copyright © 2013 Fangyan Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.