Memory pattern analysis of cellular neural networks

In this Letter, we have shown that the n-dimensional cellular neural network and delay cellular neural network can have not more than 3n memory patterns, can have 2n memory patterns which are locally exponentially stable. And we have obtained the estimates of attractive domain of such 2n locally exponentially stable memory patterns. In addition, we have derived the conditions that the equilibrium point is locally exponentially stable when the equilibrium point locate the designated position. Some sufficient conditions have been obtained to guarantee the global exponential stability for the cellular neural networks. Those conditions can be directly derived from the parameters of the neural networks, are very easy to verified. The results presented in this Letter are the improvement and extension of the existed ones. Finally, the validity and performance of the results are illustrated by two simulation results.