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- Title
Horseshoe Chaos in a 3D Neural Network with Different Activation Functions.
- Authors
Fangyan Yang; Song Tang; Guilan Xu
- 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.
- Subjects
CHAOS theory; MATHEMATICAL functions; ARTIFICIAL neural networks; LIMIT cycles; TOPOLOGY; ROBUST control; MATHEMATICAL complexes
- Publication
Discrete Dynamics in Nature & Society, 2013, p1
- ISSN
1026-0226
- Publication type
Article
- DOI
10.1155/2013/430963