Comptes Rendus
no. 7
Complexité dynamique des réseaux de Hopfield
Serge Vakulenko1
1 Institute for Mechanical Engineering Problems, Bolshoy pr. V.O. 61, St. Petersbourg, 199178 Russia
Comptes Rendus. Mathématique, Volume 335 (2002) no. 7, pp. 639-642.

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

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

Reçu le :
Révisé le :
Publié le :
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

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Complexity of gene circuits, Pfaffian functions and the morphogenesis problem

Sergey Vakulenko; Dmitry Grigoriev

C. R. Math (2003)

Separating objects and ‘neural’ computation

John J. Hopfield; Carlos D. Brody

C. R. Biol (2003)