Multistability of complex-valued neural networks with distributed delays

This paper addresses the multistability problem for the complex-valued neural networks with appropriate real–imaginary-type activation functions and distributed delays. Based on the geometrical properties of the activation functions and the fixed point theory, several sufficient criteria are obtained which not only guarantee the existence of 9^n equilibrium points but also assure the local exponential stability for the 4^n equilibrium points of them. Furthermore, the attraction basins of the 4^n equilibrium points are also estimated, which infers that the attraction basins could be enlarged under some mild restrictions. Finally, one numerical example is provided to illustrate the effectiveness of the obtained results.