### Global asymptotic stability in a class of difference equations.

Yang, Xiaofan, Cui, Limin, Tang, Yuan Yan, Cao, Jianqiu (2007)

Advances in Difference Equations [electronic only]

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Yang, Xiaofan, Cui, Limin, Tang, Yuan Yan, Cao, Jianqiu (2007)

Advances in Difference Equations [electronic only]

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The main objective of this paper is to study the boundedness character, the periodicity character, the convergence and the global stability of positive solutions of the difference equation $${x}_{n+1}=\frac{{\alpha}_{0}{x}_{n}+{\alpha}_{1}{x}_{n-l}+{\alpha}_{2}{x}_{n-k}}{{\beta}_{0}{x}_{n}+{\beta}_{1}{x}_{n-l}+{\beta}_{2}{x}_{n-k}},\phantom{\rule{1.0em}{0ex}}n=0,1,2,\cdots $$ where the coefficients ${\alpha}_{i},{\beta}_{i}\in (0,\infty )$ for $i=0,1,2,$ and $l$, $k$ are positive integers. The initial conditions ${x}_{-k},\cdots ,{x}_{-l},\cdots ,{x}_{-1},{x}_{0}$ are arbitrary positive real numbers such that $l<k$. Some numerical experiments are presented.

Li, Dongsheng, Li, Pingping, Li, Xianyi (2008)

Advances in Difference Equations [electronic only]

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Kent, Candace M., Kosmala, Witold, Stević, Stevo (2010)

Abstract and Applied Analysis

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