## Memory pattern analysis of cellular neural networks.(English)Zbl 1222.92013

Summary: We have shown that $$n$$-dimensional cellular neural networks and delay cellular neural networks can have no more than $$3n$$ memory patterns, and $$2n$$ memory patterns which are locally exponentially stable.We have obtained estimates of the attractive domain of such $$2n$$ locally exponentially stable memory patterns. In addition, we have derived conditions that the equilibrium point is locally exponentially stable when the equilibrium point is at the designated position. Some sufficient conditions have been obtained to guarantee the global exponential stability for the cellular neural networks. These conditions can be directly derived from the parameters of the neural networks, and are very easy to be verified. The results are improvements and extensions of existing ones. Finally, the validity and performance of the results are illustrated by two simulation results.

### MSC:

 92B20 Neural networks for/in biological studies, artificial life and related topics

### Keywords:

stability; equilibrium; attractive domain
Full Text:

### References:

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