Multiperiodicity and attractivity of delayed recurrent neural networks with unsaturating piecewise linear transfer functions

This paper studies multiperiodicity and attractivity for a class of recurrent neural networks (RNNs) with unsaturating piecewise linear transfer functions and variable delays. Using local inhibition, conditions for boundedness and global attractivity are established. These conditions allow coexistence of stable and unstable trajectories. Moreover, multiperiodicity of the network is investigated by using local invariant sets. It shows that under some interesting conditions, there exists one periodic trajectory in each invariant set which exponentially attracts all trajectories in that region correspondingly. Simulations are carried out to illustrate the theories.