The stable oscillatory regime in a neuron net consisting of generalized automatic neuron-detectors
Modelirovanie i analiz informacionnyh sistem, Tome 14 (2007) no. 2, pp. 30-35.

Voir la notice de l'article provenant de la source Math-Net.Ru

A new model of the neuron cell - the generalized automatic neuron (GAN) – is considered. This model has a universal character. It combines the properties of neuron-oscillator and neuron-detector. The neuron net is formed on the base of this GAN-detector. One of possible oscillatory regimes is investigated, and its stability is proved.
@article{MAIS_2007_14_2_a6,
     author = {E. V. Konovalov},
     title = {The stable oscillatory regime in a neuron net consisting of generalized automatic neuron-detectors},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {30--35},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2007_14_2_a6/}
}
TY  - JOUR
AU  - E. V. Konovalov
TI  - The stable oscillatory regime in a neuron net consisting of generalized automatic neuron-detectors
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2007
SP  - 30
EP  - 35
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2007_14_2_a6/
LA  - ru
ID  - MAIS_2007_14_2_a6
ER  - 
%0 Journal Article
%A E. V. Konovalov
%T The stable oscillatory regime in a neuron net consisting of generalized automatic neuron-detectors
%J Modelirovanie i analiz informacionnyh sistem
%D 2007
%P 30-35
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2007_14_2_a6/
%G ru
%F MAIS_2007_14_2_a6
E. V. Konovalov. The stable oscillatory regime in a neuron net consisting of generalized automatic neuron-detectors. Modelirovanie i analiz informacionnyh sistem, Tome 14 (2007) no. 2, pp. 30-35. http://geodesic.mathdoc.fr/item/MAIS_2007_14_2_a6/

[1] N. Viner, A. Rozenblyut, “Provedenie impulsov v serdechnoi myshtse”, Kiberneticheskii sbornik, 3 (1961), 3–56

[2] J. J. Hopfield, “Neural networks and physical systems mith emergent collective computational abilities”, Proc. Nat. Acad. Sci. USA, 79:8 (1982), 2554–2558 | DOI | MR

[3] V. V. Maiorov, G. V. Shabarshina, “Soobschenie o setyakh W-neironov”, Modelirovanie i analiz informatsionnykh sistem, 1997, no. 4, 37–50, Izd-vo YarGU, Yaroslavl | MR

[4] A. L. Hodgkin, A. F. Huxely, “A quantitative description of membrane current and its applications to conduction and excitation in nerve”, J. Physiol. (London), 117 (1952), 500–544

[5] J. L. Hindmarsh, R. M. Rose, “A model of neuronal bursting using three coupled first order differential equations”, Proc. R. Soc. London Ser. B, 221 (1984), 87–102 | DOI

[6] R. FitzHugh, “Impulses and physiological states in theoretical models of nerve membrane”, Biophys. J., 1 (1961), 445–466 | DOI

[7] J. S. Nagumo, S. Arimoto, S. Yoshizawa, “An active pulse transmission line simulating nerve axon”, Proc. Ire., 50 (1962), 2061–2070 | DOI

[8] S. Omata, Y. Yamaguchi, H. Shimuzi, “Entrainment among coupled limit cycle oscillator with frustration”, Physica D, 31 (1988), 397–408 | DOI | MR | Zbl

[9] H. R. Wilson, J. D. Cowan, “Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons”, Biophysical J., 12 (1972), 1–24 | DOI

[10] G. V. Shabarshina, “Provedenie vozbuzhdeniya po koltsevoi strukture neironnykh kletochnykh avtomatov”, Modelirovanie i analiz informatsionnykh sistem, 1994, no. 2, 116–121

[11] V. V. Maiorov, E. V. Konovalov, “Obobschennyi neironnyi avtomat v zadache rasprostraneniya volny vozbuzhdeniya po neironnoi seti”, IX Vserossiiskaya nauchno-tekhnicheskaya konferentsiya «Neiroinformatika-2007», Sbornik nauchnykh trudov. Ch. 3, MIFI, M., 2007, 182–188

[12] V. I. Kryukov i dr., Metastabilnye i neustoichivye sostoyaniya v mozge, Preprint, NTsBI AN SSSR, Puschino, 1986, 112 pp.

[13] N. S. Bakhvalov, N. P. Zhidkov, G. M. Kobelkov, Chislennye metody, Nauka, M., 1987, 630 pp. | MR | Zbl