Complexité dynamique des réseaux de Hopfield
Vakulenko, Serge1
1 Institute for Mechanical Engineering Problems, Bolshoy pr. V.O. 61, St. Petersbourg, 199178 Russia
Comptes Rendus. Mathématique, Tome 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.

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DOI : 10.1016/S1631-073X(02)02524-4
Vakulenko, Serge 1

1 Institute for Mechanical Engineering Problems, Bolshoy pr. V.O. 61, St. Petersbourg, 199178 Russia 
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Vakulenko, Serge. Complexité dynamique des réseaux de Hopfield. Comptes Rendus. Mathématique, Tome 335 (2002) no. 7, pp. 639-642. doi : 10.1016/S1631-073X(02)02524-4. http://www.numdam.org/articles/10.1016/S1631-073X(02)02524-4/

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

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

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

[6] Polácik, P.; Terescák, T. 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] Temam, R. Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer, 1988

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

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

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