IJPAM: Volume 105, No. 3 (2015)
LINKS BASED ON THE WATTS-STROGATZ MODEL
Department of Computational Mathematics and Informatics
South Ural State University
76 Lenin Avenue, Chelyabinsk, 454080, RUSSIA
Department of Mathematics and Physics
Chelyabinsk State Pedagogical University
69 Lenin Avenue, Chelyabinsk, 454080, RUSSIA
Abstract. We study the stability problem for a model, similar to the Watts-Strogatz model, with some parameter , ranging from 0 to 1. When , 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 , links are random with the preservation of their density. Under certain intermediate values of 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 interaction 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.
Received: September 18, 2015
AMS Subject Classification: 35Q85
Key Words and Phrases: Watts-Strogatz model, neural networks, stability, small world
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DOI: 10.12732/ijpam.v105i3.11 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 431 - 438