A mathematical and simulation model on stability and parameters of multi-equilibrium points in CNNs

In this paper, the impact of initial states on the stability in cellular neural networks (CNNs) with time delay is studied in this paper. The relationships among the parameters of CNNs are investigated and defined. Based on the relationships, the ranges of the equilibrium points of every cell in CNNs with time-delay are considered. To ensure that n-cell cellular neural networks are locally stable, sufficient conditions are obtained. Furthermore, a design procedure of parameters of CNNs for associative memories is given. Finally, numerical simulations are presented to support the effectiveness of the theoretical analysis. The results in the paper can be used in associative memories.