A Hopfield neural network with multi-compartmental activation

AKHMET M., Karacaoren M.

NEURAL COMPUTING & APPLICATIONS, cilt.29, sa.10, ss.815-822, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 10
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s00521-016-2597-9
  • Dergi Adı: NEURAL COMPUTING & APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.815-822
  • Anahtar Kelimeler: Hopfield neural networks, Equilibrium, Exponential stability, Piecewise constant argument of generalized type, Constant delay, Linear matrix inequality, TIME-VARYING DELAYS, GLOBAL ASYMPTOTIC STABILITY, CONTINUOUSLY DISTRIBUTED DELAYS, PIECEWISE-CONSTANT ARGUMENT, EXPONENTIAL STABILITY, ASSOCIATIVE MEMORY, ROBUST STABILITY, TRANSMISSION DELAYS, CONVERGENCE RATE, DISCRETE
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

The Hopfield network is a form of recurrent artificial neural network. To satisfy demands of artificial neural networks and brain activity, the networks are needed to be modified in different ways. Accordingly, it is the first time that, in our paper, a Hopfield neural network with piecewise constant argument of generalized type and constant delay is considered. To insert both types of the arguments, a multi-compartmental activation function is utilized. For the analysis of the problem, we have applied the results for newly developed differential equations with piecewise constant argument of generalized type beside methods for differential equations and functional differential equations. In the paper, we obtained sufficient conditions for the existence of an equilibrium as well as its global exponential stability. The main instruments of investigation are Lyapunov functionals and linear matrix inequality method. Two examples with simulations are given to illustrate our solutions as well as global exponential stability.