A note on chaotic behavior in simple neural networks.

Local dynamics in a neural network are described by a two-dimensional (backpropagation or Hebbian) map of network activation and coupling strength. Adiabatic reduction leads to a non-linear one-dimensional map of coupling strength, suggesting the presence of a period-doubling route to chaos. It is shown that smooth variation of one of the parameters of the original map, -learning rate-, gives rise to period-doubling bifurcations of total coupling strength. Firstly, the associated bifurcation diagrams are given which indicate the presence of chaotic regimes and periodic windows. Secondly, pseudo-phase spacediagrams and the Lyapunov exponents for alleged chaotic regimes are presented. Finally, spectral plots associated with these regimes are shown.