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.
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.