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Dynamics of a Class of Higher Order Difference Equations

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  • Bratislav D. Iricanin

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 .

Suggested Citation

  • Bratislav D. Iricanin, 2007. "Dynamics of a Class of Higher Order Difference Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2007, pages 1-6, February.
    • Handle: RePEc:hin:jnddns:073849
    DOI: 10.1155/2007/73849
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    1. Liu, Pingzhou & Cui, Xiaoying, 2000. "Hyperbolic logistic difference equation with infinitely many delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 52(3), pages 231-250.
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