Artificial intelligence

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ISSN 2710-1673

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The convergence of neurodynamics processes in the hopfield mode

Shatyrko A.1, Khusainov D.1, Diblik J.3, Bashtinec J.4
1 Kyiv National Taras Shevchenko University
3 Brno University of Technology, CEITEC - Central European Institute of Technology
4 Brno University of Technology, CEITEC - Central European Institute of Technology

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UDC: 517.929
Publication Language: Russian
Stuc. intelekt. 2017; 22(3-4):139-148

Abstract: Mathematical models of the dynamics of a neural network, which are represented by systems of ordinary differential equations, as well as differential equations with time-delay argument and the distinguished asymptotically stable linear part are considered. With the using of the direct Lyapunov method, sufficient conditions for asymptotic stability are obtained and exponential estimates of the solutions decay are constructed. The results are formulated in the form of matrix algebraic inequalities.

Keywords: neuronet, stability, Lyapunov’s method, time-delay argument

References:

  1. Amosov N.M. Algoritmy razuma. – Kiev, Naukova dumka. – 1985. (Glushkov V.M. - ВА 145)
  2. McCulloch W.S., Pitts W. "А logical calculus of the ideas immanent in nervous activity" // Bulletin of Mathematica1 Biophysics, 1943, vоl. 5, р. 115-133.
  3. McCulloch W.S., Pitts W. Logicheskoe ischislenie idey, otnosyschihsya k nervnoy aktivnosti. – V sb. Galushkina A.I., Tsypkin Ya.Z. Neyronniye seti: Istoriya razvitiya teorii, kn. 5. – М., IPRZhR, 2001. – 840 s.
  4. Haykin S. Neyronnie seti:polniy kurs, 2 izdanie, М.: Izdatelskiy dom «Wilyams», 2006. – 1104 s.
  5. Hopfield J.J. Neurons with graded response have collective computational properties like those of two state neurons // Proceedings of the National Academy of Sciences, USA, 1984, vоl. 81, р. 3088-3092.
  6. Rall W. Cable theory for dendritic neurons. In Methods in Neuronal Modeling, С. Koch and I. Segev, eds., 1989, р. 9-62, Cambridge, МА: MIТ Press.
  7. Gopalsamy K. Leakage Delays in BAM // Journal of Mathematical Analysis and Applications, 325 (2007), pp. 1117-1132.
  8. El’sgol’ts L.E., Norkin S.B. Introduction to the theory of the differential equations with deviating argument. – Academic Press, New York, 1973.
  9. Razumikhin B.S. Ob ustoychivosti system s zapazdivaniem // B.S. Razumikhin – Prikladnaya matematika i mechanica, V.20, No4, 1956. – S. 500-512.

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