Abstract
We study the stability problem for a model, similar to the Watts- Strogatz model, with some parameter p, ranging from 0 to 1. When p = 0, the model is a deterministic model of a ring delayed neural network in which each neuron is connected to several neighbors in the ring. When p = 1, links are random with the preservation of their density. Under certain intermediate values of p we obtain the small world neural network. We find out whether the stability of the model in this process is improved. Our numerical experiments give a double response: if the forces of inter- action between the different network nodes are the same, then the transition from deterministic to random network contributes to the loss of stability; if the forces are substantially different, then the stability region increases. This response refines the previously known results on the stability of small world type networks.
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