IJPAM: Volume 76, No. 3 (2012)

NUMERICAL AND QUALITATIVE STABILITY ANALYSIS
OF RING AND LINEAR NEURAL NETWORKS WITH
A LARGE NUMBER OF NEURONS

Tatyana Khokhlova$^1$, Mikhail Kipnis$^2$
$^{1,2}$Department of Mathematics
South Ural State University
Chelyabinsk, 454080, RUSSIA
$^2$Department of Mathematics
Chelyabinsk State Pedagogical University
Chelyabinsk 454080, RUSSIA


Abstract. We describe the stability domain in the parameter space of a ring neural network with an unlimited number of neurons by means of the stability cones. We found that the stability domain expands, when the ring of neurons is broken. Networks are described by matrix delay differential higher order equations.

Received: December 10, 2011

AMS Subject Classification: 35A11

Key Words and Phrases: neural networks, delay differential matrix equations, stability cone, delay-independent stability

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 76
Issue: 3