The stability of the 2n-element number neural network models

In this paper, we defined a energy function for the 2n-element number neural network models with n < 3. It is proved that the memorized patterns are local minima of the energy function. In the case of random purely sequential dynamics, the energy of the network decreases monotonically with time and so the nonlinear 2n-element number neural network with n < 3 must end up in a state of equilibrium, which is stable against changes in the state of any single neuron.