IJPAM: Volume 105, No. 3 (2015)

ON THE STABILITY OF A NEURAL NETWORK WITH
LINKS BASED ON THE WATTS-STROGATZ MODEL

Sergey Ivanov$^1$, Mikhail Kipnis$^{2}$
$^1$Department of Computational Mathematics and Informatics
South Ural State University
76 Lenin Avenue, Chelyabinsk, 454080, RUSSIA
$^2$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 $p$, 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 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
Year: 2015
Volume: 105
Issue: 3
Pages: 431 - 438


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