Dynamics of a Higher-Order Nonlinear Difference Equation

Guo-Mei Tang, Lin-Xia Hu and Xiu-Mei Jia

Discrete Dynamics in Nature and Society, 2010, vol. 2010, 1-15

Abstract:

We consider the higher-order nonlinear difference equation ð ‘¥ ð ‘› + 1 = ( ð ›¼ + ð ‘¥ ð ‘› ) / ( ð ´ + ð µ ð ‘¥ ð ‘› + ð ‘¥ ð ‘› − 𠑘 ) , ð ‘› = 0 , 1 , … , where parameters are positive real numbers and initial conditions ð ‘¥ − 𠑘 , … , ð ‘¥ 0 are nonnegative real numbers, 𠑘 ≥ 2 . We investigate the periodic character, the invariant intervals, and the global asymptotic stability of all positive solutions of the abovementioned equation. We show that the unique equilibrium of the equation is globally asymptotically stable under certain conditions.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:534947

DOI: 10.1155/2010/534947

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