Complex Systems

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

Xin Wang
Department of Mathematics, University of Southern California,
Los Angeles, CA 90089-1113, USA


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 situations. 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 the existence of period-doublings to chaos and strange attractors in the network.