References
J. J. Hopfield, "Neural networks and physical systems with emergent collective computational abilities," Proc. Natl. Acad. Sci. USA,79, No. 8, 2554–2558 (1982).
A. N. Chetaev, Neural Networks and Markov Chains [in Russian], Nauka, Moscow (1985).
P. Peretto and J. J. Nietz, "Stochastic dynamics of neural networks," IEEE Trans. Syst. Man Cybern.,SMC-16, No. 1, 73–83 (1986).
M. N. Oguztoreli, G. M. Steil, and T. M. Caelli, "Control mechanisms of a neural network," Biol. Cybern.,54, No. 1, 21–28 (1986).
K. Matsuoka, "Sustained oscillations generated by mutually inhibiting neurons with adaptation," Biol. Cybern.,52, No. 6, 367–376 (1985).
A. Lapedes and R. Farber, "A self-optimizing, nonsymmetrical neural net for content addressable memory and pattern recognition," Physica D: Nonlinear Phenomena,22D, No. 1–3, 247–259 (1986).
S. N. Vorob'eva and A. B. Piunovskii, "Dynamic model of a two-layer stochastic neural net," in: Relaxation Processes and Phenomena in Active Media [in Russian], IFTP, Moscow (1990), pp. 63–69.
S. V. Fomin and M. B. Berkinblit, Mathematical Problems in Biology, [in Russian], Nauka, Moscow (1973).
A. A. Bondar, "On probabilistic character of the transformation of information by a neuron," Proc. of Symposium on Statistical Electrophysiology [in Russian], Part 1, VGU, Vil'nyus (1968), pp. 81–92.
I. V. Popov, "On input pulse streams of visual analyzer neurons," Probl. Neirokibern.,2, 64–68 (1966).
A. B. Kogan and I. V. Popov, "On transformation of stationary Poisson pulse stream in the nerve cell synapse," Probl. Neirokibern.,2, 42–45 (1966).
W. Feller, An Introduction to Probability Theory and Its Applications [Russian translation], Vol. 2, Mir, Moscow (1984).
R. Elliott, Stochastic Analysis and Its Applications [Russian translation], Mir, Moscow (1986).
R. Sh. Liptser and A. N. Shiryaev, Martingale Theory [in Russian], Nauka, Moscow (1986).
V. A. Trenogin, Functional Analysis [in Russian], Nauka, Moscow (1980).
A. A. Yushkevich, "Continuous-time controlled Markov models with countably many sets," Teor. Verotyatn. Primenen.,22, No. 2, 222–241 (1977).
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Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 22–34, November–December, 1993.
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Piunovskii, A.B. Analysis of pulse frequency in a simple neural network. Cybern Syst Anal 29, 798–808 (1993). https://doi.org/10.1007/BF01122732
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DOI: https://doi.org/10.1007/BF01122732