Abstract
We show that in discrete models of Hopfield type some properties of global stability and chaotic behaviour are coded in the dynamics of a related one-dimensional equation. Using this fact, we obtain some new results on stability and chaos for a system of delayed neural networks; some relevant properties of our results are that we do not require monotonicity properties in the activation function, we allow any architecture of the network, and the conclusions are independent of the size of the time delays.
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