Discrete Dynamics in Nature and Society

Discrete Dynamics in Nature and Society / 2007 / Article

Research Article | Open Access

Volume 2007 |Article ID 089413 | https://doi.org/10.1155/2007/89413

Stevo Stevic, "Permanence for a Generalized Discrete Neural Network System", Discrete Dynamics in Nature and Society, vol. 2007, Article ID 089413, 9 pages, 2007. https://doi.org/10.1155/2007/89413

Permanence for a Generalized Discrete Neural Network System

Received07 Nov 2006
Revised31 Jan 2007
Accepted05 Feb 2007
Published14 Mar 2007

Abstract

We prove that the system of difference equations xn+1(i)=λixn(i)+fi(αixn(i+1)βixn1(i+1)), i{1,2,,k}, n, (we regard that xn(k+1)=xn(1)) is permanent, provided that αiβi, λi+1[0,βi/αi), i{1,2,,k}, fi:, i{1,2,,k}, are nondecreasing functions bounded from below and such that there are δi(0,1) and M>0 such that fi(αix)δix, i{1,2,,k}, for all xM. This result considerably extends the results existing in the literature. The above system is an extension of a two-dimensional discrete neural network system.

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Copyright © 2007 Stevo Stević. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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