Self-excited oscillations and period doubling condition in Hopfield neural network

A simple dynamic neural network is considered. The behavior of neural network is investigated by analyzing the associated characteristic equation for the case of exterior influence absence and for the case of exterior influence action. It is shown that for the first case the system that consists of two neurons can generate self-excited oscillations and for the second case the condition for period doubling was obtained. It is shown that for dynamical neural networks exist simple mechanisms for chaos appearance for the network as a whole.