Global Stability of a Rational Difference Equation

Guo-Mei Tang, Lin-Xia Hu and Gang Ma

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

Abstract:

We consider the higher-order nonlinear difference equation ð ‘¥ ð ‘› + 1 = ( ð ‘ + ð ‘ž ð ‘¥ ð ‘› − 𠑘 ) / ( 1 + ð ‘¥ ð ‘› + ð ‘Ÿ ð ‘¥ ð ‘› − 𠑘 ) , ð ‘› = 0 , 1 , … with the parameters, and the initial conditions ð ‘¥ − 𠑘 , … , ð ‘¥ 0 are nonnegative real numbers. We investigate the periodic character, invariant intervals, and the global asymptotic stability of all positive solutions of the above-mentioned equation. In particular, our results solve the open problem introduced by Kulenović and Ladas in their monograph (see Kulenović and Ladas, 2002).

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:432379

DOI: 10.1155/2010/432379

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