Global Behavior of a Higher-Order Difference Equation

Tuo Li and Xiu-Mei Jia

Discrete Dynamics in Nature and Society, 2010, vol. 2010, 1-8

Abstract:

This paper is concerned with the global behavior of higher-order difference equation of the form 𠑦 𠑛 + 1 = ( 𠑦 𠑛 ∑ e x p ( 𠛽 ( 1 − 2 𠑘 𠑖 = 0 𠑎 𠑖 𠑦 𠑛 − 𠑖 ) ) ) / ( 1 − 𠑦 𠑛 + 𠑦 𠑛 ∑ e x p ( 𠛽 ( 1 − 2 𠑘 𠑖 = 0 𠑎 𠑖 𠑦 𠑛 − 𠑖 ) ) ) , 𠑛 = 0 , 1 , 2 … , 𠑦 − 𠑘 , 𠑦 − 𠑘 + 1 , … , 𠑦 0 ∈ ( 0 , 1 ) . Under some certain assumptions, it is proved that the positive equilibrium is globally asymptotical stable.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:834020

DOI: 10.1155/2010/834020

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