Permanence for a Generalized Discrete Neural Network System

Stevo Stevic

Discrete Dynamics in Nature and Society, 2007, vol. 2007, 1-9

Abstract:

We prove that the system of difference equations x n + 1 ( i ) = λ i x n ( i ) + f i ( α i x n ( i + 1 ) − β i x n − 1 ( i + 1 ) ) , i ∈ { 1 , 2 , … , k } , n ∈ ℕ , (we regard that x n ( k + 1 ) = x n ( 1 ) ) is permanent, provided that α i ≥ β i , λ i + 1 ∈ [ 0 , β i / α i ) , i ∈ { 1 , 2 , … , k } , f i : ℠→ ℠, i ∈ { 1 , 2 , … , k } , are nondecreasing functions bounded from below and such that there are δ i ∈ ( 0 , 1 ) and M > 0 such that f i ( α i x ) ≤ δ i x , 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.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:089413

DOI: 10.1155/2007/89413

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