Period-Doublings to Chaos in a Simple Neural Network: An Analytical Proof.

Abstract

The dynamics of discrete-time neural networks with the sigmoid function as neuron activation function can be extraordinarily complex as some authors have displayed in numerical simulations. Here we consider a simple neural network of only two neurons, one excitatory and the other inhibitory, with no external inputs and no time delay as a parameterized family of two dimensional maps, and give an analytical proof for existence of period-doublings to chaos and strange attractors in the network.