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Dynamics of a Higher-Order Nonlinear Difference Equation

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  • Guo-Mei Tang
  • Lin-Xia Hu
  • Xiu-Mei Jia

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.

Suggested Citation

  • Guo-Mei Tang & Lin-Xia Hu & Xiu-Mei Jia, 2010. "Dynamics of a Higher-Order Nonlinear Difference Equation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-15, September.
    • Handle: RePEc:hin:jnddns:534947
    DOI: 10.1155/2010/534947
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