Horseshoe Chaos in a 3D Neural Network with Different Activation Functions
Joint Authors
Xu, Guilan
Yang, Fangyan
Tang, Song
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-04-28
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Yang, Fangyan& Tang, Song& Xu, Guilan. 2013. Horseshoe Chaos in a 3D Neural Network with Different Activation Functions. Discrete Dynamics in Nature and Society،Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-471715
Modern Language Association (MLA)
Yang, Fangyan…[et al.]. Horseshoe Chaos in a 3D Neural Network with Different Activation Functions. Discrete Dynamics in Nature and Society No. 2013 (2013), pp.1-6.
https://search.emarefa.net/detail/BIM-471715
American Medical Association (AMA)
Yang, Fangyan& Tang, Song& Xu, Guilan. Horseshoe Chaos in a 3D Neural Network with Different Activation Functions. Discrete Dynamics in Nature and Society. 2013. Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-471715
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-471715