The dynamics of nonlinear systems consisting of a huge number of interacting particles usually are dealt with by partial differential equations. Here the system consists of a neural network the recall and learning processes of which are to be described. The basic variables for the dynamics of a neural network are the time t, the states y of the neurons and the states W of the weights. The dynamics of the states is influenced by four sources: external inputs, neuron model, network topology and physical implementation. The external inputs may be comprised of reference signals for learning as well as actual input signals; the neuron be modeled by an algebraic equation, an ordinary differential equation or a system of partial differential equations, depending on how closely the model is to fit the biological neurons. First and second order ordinary differential equations are considered, for they help achieve stability in recurrent networks as well as in electronic implementations of neural nets.
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