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A Hopfield neural network with multi-compartmental activation
Date
2018-05-01
Author
Akhmet, Marat
Karacaoren, Meltem
Metadata
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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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.
Subject Keywords
Software
,
Artificial Intelligence
URI
https://hdl.handle.net/11511/39309
Journal
NEURAL COMPUTING & APPLICATIONS
DOI
https://doi.org/10.1007/s00521-016-2597-9
Collections
Department of Mathematics, Article