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. Adiabetic reduction leads to a nonlinear 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 space diagrams and the Lyapunov exponents for alleged chaotic regimes are presented. Finally, spectral plots associated with these regimes are shown.