Dynamics of a Class of Higher Order Difference Equations

Bratislav D. Iricanin

Discrete Dynamics in Nature and Society, 2007, vol. 2007, 1-6

Abstract:

We prove that all positive solutions of the autonomous difference equation x n = α x n − k / ( 1 + x n − k + f ( x n − 1 , … , x n − m ) ) ,   n ∈ ℕ 0 , where k , m ∈ ℕ , and f is a continuous function satisfying the condition β   min { u 1 , … , u m } ≤ f ( u 1 , … , u m ) ≤ β   max { u 1 , … , u m } for some β ∈ ( 0 , 1 ) , converge to the positive equilibrium x ¯ = ( α − 1 ) / ( β + 1 ) if α > 1 .

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:073849

DOI: 10.1155/2007/73849

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