Multistability of neural networks with discontinuous activation function

In this paper, the multistability is studied for two-dimensional neural networks with multilevel activation functions. And it is showed that the system has n2 isolated equilibrium points which are locally exponentially stable, where the activation function has n segments. Furthermore, evoked by periodic external input, n2 periodic orbits which are locally exponentially attractive, can be found. And these results are extended to k-neuron networks, which is really enlarge the capacity of the associative memories. Examples and simulation results are used to illustrate the theory.