Asymptotic behaviour of neural networks

A new method is presented for analysing the global stability properties of neural networks. An efficient and numerically robust procedure is developed for estimating regions of asymptotic stability. The method combines Liapunov theory, simulation in reverse time and some topological properties of the true stability region. The result is an accurate estimate of the true stability boundary. The main limitation of the method is that a global Liapunov function for the neural network must be found, fortunately large classes of neural networks possess such a Liapunov function.