一类时滞Logistic差分方程的全局吸引性 Global attractivity in a delay logistic difference equation期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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一类时滞Logistic差分方程的全局吸引性

引用本文：

周英告.一类时滞Logistic差分方程的全局吸引性[J].高校应用数学学报(英文版),2003,18(1):53-58.

作者姓名：

周英告

作者单位：

Zhou YinggaoDept. of Appl.Math.and Appl.Software,Central South Univ.,Changsha 410083,China.

基金项目：

theNationalNaturalScienceFoundationofChina (198310 30 ) .

摘要：

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｎｏｎａｕｔｏｎｏｍｏｕｓｄｅｌａｙｌｏｇｉｓｔｉｃｄｉｆｆｅｒｅｎｃｅｅｑｕａｔｉｏｎΔｙｎ =ｐｎｙｎ( 1 - ｙτ(ｎ) )　 ,ｎ =0 ,1 ,2 ,...,( 1 1 )ｗｈｅｒｅｐｎ ∞ｎ =0 ｉｓａｓｅｑｕｅｎｃｅｏｆｐｏｓｉｔｉｖｅｒｅａｌｎｕｍｂｅｒｓ ,τ(ｎ) ∞ｎ =0 ｉｓａｎｏｎｄｅｃｒｅａｓｉｎｇｓｅｑｕｅｎｃｅｏｆｉｎｔｅｇｅｒｓ,τ(ｎ) <ｎａｎｄｌｉｍｎ→∞τ(ｎ) =∞ ,Δｙｎ=ｙｎ +1- ｙｎ.Ｍｏｔｉｖａｔｅｄｂｙｐｌａｕｓｉｂｌｅａｐｐｌｉｃａｔｉｏｎｓ…

Global attractivity in a delay logistic difference equation

Zhou Yinggao.Global attractivity in a delay logistic difference equation[J].Applied Mathematics A Journal of Chinese Universities,2003,18(1):53-58.

Authors:

Zhou Yinggao

Institution:

(1) Dept. of Appl. Math. and Appl. Software, Central South Univ., 410083 Changsha, China

Abstract:

This paper studies the global attractivity of the positive equilibrium 1 of the delay logistic difference equation

$\vartriangle y_n = p_n y_n \left( {1 - y_{\tau \left( n \right)} } \right), n = 0, 1, 2, . . .,$

(*)

where {p _n} is a sequence of positive real numbers, {τ(n)} is a nondecreasing sequence of integers, τ(n)<n and $\mathop {\lim }\limits_{x \to \infty } \tau \left( n \right) = \infty$ . It is proved that if

$\sum\limits_{j = \tau \left( n \right)}^n {p_j \leqslant \frac{5}{4}} for sufficiently large n and \sum\limits_{j = 0}^\infty {p_j = \infty ,}$

then all positive solutions of Eq. (*) tend to 1 as n → ∞. The results improve the existing results in literature. Supported by the National Natural Science Foundation of China (19831030).

Keywords:

global attractivity positive solutions logistic delay difference equation

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