Permanence for a Generalized Discrete Neural Network System
We prove that the system of difference equations xn+1(i)=λixn(i)+fi(αixn(i+1)−βixn−1(i+1)), i∈{1,2,…,k}, n∈ℕ, (we regard that xn(k+1)=xn(1)) is permanent, provided that αi≥βi, λi+1∈[0,βi/αi), i∈{1,2,…,k}, fi:ℝ→ℝ, i∈{1,2,…,k}, are nondecreasing functions bounded from below and such that there are δi∈...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2007/89413 |
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| author | Stevo Stevic |
| author_facet | Stevo Stevic |
| author_sort | Stevo Stevic |
| collection | DOAJ |
| description | We prove that the system of difference equations xn+1(i)=λixn(i)+fi(αixn(i+1)−βixn−1(i+1)), i∈{1,2,…,k}, n∈ℕ, (we regard that xn(k+1)=xn(1)) is permanent, provided that αi≥βi, λi+1∈[0,βi/αi), i∈{1,2,…,k}, fi:ℝ→ℝ, 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 x≥M. This result considerably extends the results existing in the literature. The above system is an extension of a two-dimensional discrete neural network system. |
| format | Article |
| id | doaj-art-66e8d08024ca4d519b48bc3d0a1c4074 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-66e8d08024ca4d519b48bc3d0a1c40742025-02-03T05:57:53ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2007-01-01200710.1155/2007/8941389413Permanence for a Generalized Discrete Neural Network SystemStevo Stevic0Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 35/I, Beograd 11000, SerbiaWe prove that the system of difference equations xn+1(i)=λixn(i)+fi(αixn(i+1)−βixn−1(i+1)), i∈{1,2,…,k}, n∈ℕ, (we regard that xn(k+1)=xn(1)) is permanent, provided that αi≥βi, λi+1∈[0,βi/αi), i∈{1,2,…,k}, fi:ℝ→ℝ, 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 x≥M. This result considerably extends the results existing in the literature. The above system is an extension of a two-dimensional discrete neural network system.http://dx.doi.org/10.1155/2007/89413 |
| spellingShingle | Stevo Stevic Permanence for a Generalized Discrete Neural Network System Discrete Dynamics in Nature and Society |
| title | Permanence for a Generalized Discrete Neural Network System |
| title_full | Permanence for a Generalized Discrete Neural Network System |
| title_fullStr | Permanence for a Generalized Discrete Neural Network System |
| title_full_unstemmed | Permanence for a Generalized Discrete Neural Network System |
| title_short | Permanence for a Generalized Discrete Neural Network System |
| title_sort | permanence for a generalized discrete neural network system |
| url | http://dx.doi.org/10.1155/2007/89413 |
| work_keys_str_mv | AT stevostevic permanenceforageneralizeddiscreteneuralnetworksystem |