Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation

Xiu-Mei Jia and Wan-Tong Li

Discrete Dynamics in Nature and Society, 2010, vol. 2010, 1-17

Abstract:

We investigate the local stability, prime period-two solutions, boundedness, invariant intervals, and global attractivity of all positive solutions of the following difference equation: 𠑦 ð ‘› + 1 = ( ð ‘Ÿ + ð ‘ ð ‘¦ ð ‘› + 𠑦 ð ‘› − 𠑘 ) / ( ð ‘ž 𠑦 ð ‘› + 𠑦 ð ‘› − 𠑘 ) , ð ‘› ∈ â„• 0 , where the parameters ð ‘ , ð ‘ž , ð ‘Ÿ ∈ ( 0 , ∞ ) , 𠑘 ∈ { 1 , 2 , 3 , … } and the initial conditions 𠑦 − 𠑘 , … , 𠑦 0 ∈ ( 0 , ∞ ) . We show that the unique positive equilibrium of this equation is a global attractor under certain conditions.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:610467

DOI: 10.1155/2010/610467

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