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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

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