Multi-stability and almost periodic solutions of a class of recurrent neural networks

This paper studies multi-stability, existence of almost periodic solutions of a class of recurrent neural networks with bounded activation functions. After introducing a sufficient condition insuring multi-stability, many criteria guaranteeing existence of almost periodic solutions are derived using Mawhin’s coincidence degree theory. All the criteria are constructed without assuming the activation functions are smooth, monotonic or Lipschitz continuous, and that the networks contains periodic variables (such as periodic coefficients, periodic inputs or periodic activation functions), so all criteria can be easily extended to fit many concrete forms of neural networks such as Hopfield neural networks, or cellular neural networks, etc. Finally, all kinds of simulations are employed to illustrate the criteria.