The stability domain in the parameters space of recursive neural networks with hypercube topology
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 7 (2012), pp. 157-160 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The stability conditions are described for the discrete neural networks. The stability domains in the parameters space are constructed. The problem is reduced to the stability problem of finite-difference matrix equations of higher order with delay. The main method to solve the problem is the stability cone.
Keywords: neural networks, finite-difference matrix equations, finite-difference equations stability
Mots-clés : hypercube.
@article{VYURM_2012_7_a23,
     author = {S. A. Ivanov},
     title = {The stability domain in the parameters space of recursive neural networks with hypercube topology},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {157--160},
     year = {2012},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2012_7_a23/}
}
TY  - JOUR
AU  - S. A. Ivanov
TI  - The stability domain in the parameters space of recursive neural networks with hypercube topology
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
PY  - 2012
SP  - 157
EP  - 160
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/VYURM_2012_7_a23/
LA  - ru
ID  - VYURM_2012_7_a23
ER  - 
%0 Journal Article
%A S. A. Ivanov
%T The stability domain in the parameters space of recursive neural networks with hypercube topology
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
%D 2012
%P 157-160
%N 7
%U http://geodesic.mathdoc.fr/item/VYURM_2012_7_a23/
%G ru
%F VYURM_2012_7_a23
S. A. Ivanov. The stability domain in the parameters space of recursive neural networks with hypercube topology. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 7 (2012), pp. 157-160. http://geodesic.mathdoc.fr/item/VYURM_2012_7_a23/

[1] A. Gonzalez, M. Valero-Garcia, L. Diaz de Cerio, “Executing algorithms with hypercube topology on torus multicomputers”, IEEE Transactions on parallel and distributed systems, 6:8 (1995), 803–814 | DOI

[2] Y. Yuan, S. A. Campbell, “Stability and synchronization ring of identical cells with delayed coupling”, J. of Dynamics and Differential Equations, 16 (2004), 709–744 | DOI | MR | Zbl

[3] E. Kaslik, “Dynamics of a discrete-time bidirectional ring of neurons with delay”, Proceedings of Int. Joint Conf. on neural networks (Atlanta, Georgia, USA, June 14–19), IEEE Computer society press, 2009, 1539–1546

[4] E. Kaslik, “Stability results for a class of difference systems with delay”, Advances in Difference Equations, 2009, 938492, 1–13 | MR

[5] F. Botelho, V. Gaiko, “Global analysis of planar networks”, Nonlinear Analysis, 64:5 (2006), 1002–1011 | DOI | MR | Zbl

[6] T. N. Kokhlova, M. M. Kipnis, “Stability of a ring and linear neural networks with a large number of neurons”, Applied Mathematics and Computation, 2012, 1–14

[7] S. A. Ivanov, M. M. Kipnis, V. V. Malygina, “The stability cone for a difference matrix equation with two delays”, ISRN J. Applied Mathematics, 2011, 910936, 1–19 | DOI | MR

[8] M. M. Kipnis, V. V. Malygina, “The stability cone for a matrix delay difference equation”, International J. of Mathematics and Mathematical Sciences, 2011, 860326, 1–15 | DOI | MR

[9] T. N. Khokhlova, M. M. Kipnis, V. V. Malygina, “The stability cone for a delay differential matrix equation”, Applied Math. Lett., 24 (2011), 742–745 | DOI | MR | Zbl