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

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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.
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/
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[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