Comptes Rendus
Complexité dynamique des réseaux de Hopfield
[Dynamical complexity of the Hopfield networks]
Comptes Rendus. Mathématique, Volume 335 (2002) no. 7, pp. 639-642.

One considers the Hopfield networks. It is shown that this system can generate any structurally stable inertial dynamics, with a bounded memory.

On considère les réseaux de neurones de Hopfield. On montre que ce système peut engendrer toute dynamique inertielle structurellement stable, avec mémoire bornée.

Received:
Revised:
Published online:
DOI: 10.1016/S1631-073X(02)02524-4

Serge Vakulenko 1

1 Institute for Mechanical Engineering Problems, Bolshoy pr. V.O. 61, St. Petersbourg, 199178 Russia
@article{CRMATH_2002__335_7_639_0,
     author = {Serge Vakulenko},
     title = {Complexit\'e dynamique des r\'eseaux de {Hopfield}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {639--642},
     publisher = {Elsevier},
     volume = {335},
     number = {7},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02524-4},
     language = {fr},
}
TY  - JOUR
AU  - Serge Vakulenko
TI  - Complexité dynamique des réseaux de Hopfield
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 639
EP  - 642
VL  - 335
IS  - 7
PB  - Elsevier
DO  - 10.1016/S1631-073X(02)02524-4
LA  - fr
ID  - CRMATH_2002__335_7_639_0
ER  - 
%0 Journal Article
%A Serge Vakulenko
%T Complexité dynamique des réseaux de Hopfield
%J Comptes Rendus. Mathématique
%D 2002
%P 639-642
%V 335
%N 7
%I Elsevier
%R 10.1016/S1631-073X(02)02524-4
%G fr
%F CRMATH_2002__335_7_639_0
Serge Vakulenko. Complexité dynamique des réseaux de Hopfield. Comptes Rendus. Mathématique, Volume 335 (2002) no. 7, pp. 639-642. doi : 10.1016/S1631-073X(02)02524-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02524-4/

[1] L. Alvarez; F. Guichard; P.L. Lions; J.M. Morel Axioms and fundamental equations of image processing, Arch. Rational Mech. Anal., Volume 16 (1993), pp. 200-257

[2] N.O. Brunel; O. Truillier Plasticity of directional place fields in a model of rodent CA3, Hippocampus, Volume 8 (1998), pp. 651-665

[3] V. Caselles, B. Coll, J.M. Morel, Partial differential equations and image processing, Séminaire Équations aux Dérivées Partielles, École polytechnique, Exp. XXI (1995–1996) XXI-1–XXI-30.

[4] K. Funahashi; Y. Nakamura The approximation of dynamical systems by continuous time reccurent neural networks, Neural Networks, Volume 6 (1993), pp. 801-806

[5] K. Hornik; M. Stinchcombe; H. White Multilayered feedforward networks are universal approximators, Neural Networks, Volume 2 (1989), pp. 359-366

[6] P. Polácik; T. Terescák Convergence to cycles as a typical asymptotic behaviour in smooth strongly monotone dicrete-time dynamical systems, Arch. Rational Mech. Anal., Volume 116 (1991), pp. 339-360

[7] R. Temam Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer, 1988

[8] S. Vakulenko Dissipative systems generating any structurally stable chaos, Adv. Differential Equations, Volume 5 (2000), pp. 1139-1178

[9] S. Vakulenko; P. Gordon Neural networks with prescribed large time behaviour, J. Phys. A, Volume 31 (1998), pp. 9555-9570

Cited by Sources:

Comments - Policy