| 赵斌.两类广泛递归序列的动力特性[J].数学研究及应用,2010,30(5):929~935 |
| 两类广泛递归序列的动力特性 |
| Dynamics of Two Extensive Classes of Recursive Sequences |
| 投稿时间：2008-08-23 修订日期：2009-01-05 |
| DOI：10.3770/j.issn:1000-341X.2010.05.022 |
| 中文关键词: 递归序列 平衡点 动力特性. |
| 英文关键词:recursive sequence equilibrium dynamics. |
| 基金项目:国家自然科学基金(No.10771169). |
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| 摘要点击次数: 2418 |
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| 中文摘要: |
| 研究了两类广泛递归序列:$$x_{n 1}={c\sum\limits_{j=0}^{k}\sum\limits_{( i_0,i_1,\ldots, i_{2j})\in A_{2j}}x_{n-i_0}x_{n-i_1}\cdots x_{n-i_{2j}} f(x_{n-i_0}, x_{n-i_1}, \ldots, x_{n-i_{2k}})\over c\sum\limits_{j=1}^{k}\sum\limits_{( i_0,i_1,\ldots, i_{2j-1})\in A_{2j-1}}x_{n-i_0}x_{n-i_1}\cdots x_{n-i_{2j-1}} c f(x_{n-i_0}, x_{n-i_1}, \ldots, x_{n-i_{2k}})}$$和$$x_{n 1}={c\sum\limits_{j=1}^{k}\sum\limits_{( i_0, i_1,\ldots, i_{2j-1})\inA_{2j-1}}x_{n-i_0}x_{n-i_1}\cdots x_{n-i_{2j-1}} c f(x_{n-i_0}, x_{n-i_1}, \ldots, x_{n-i_{2k}})\over c\sum\limits_{j=0}^{k}\sum\limits_{( i_0, i_1,\ldots, i_{2j})\in A_{2j}}x_{n-i_0}x_{n-i_1}\cdots x_{n-i_{2j}} f(x_{n-i_0}, x_{n-i_1}, \ldots, x_{n-i_{2k}})}$$的动力特性, 证明了它们的唯一正平衡点$\overline{x} =1$是全局渐近稳定的, 为递归序列理论的研究提供了一种新的途径. |
| 英文摘要: |
| We investigate the dynamics of two extensive classes of recursive sequences:$$x_{n 1}={c\sum\limits_{j=0}^{k}\sum\limits_{( i_0,i_1,\ldots, i_{2j})\in A_{2j}}x_{n-i_0}x_{n-i_1}\cdots x_{n-i_{2j}} f(x_{n-i_0}, x_{n-i_1}, \ldots, x_{n-i_{2k}})\over c\sum\limits_{j=1}^{k}\sum\limits_{( i_0,i_1,\ldots, i_{2j-1})\in A_{2j-1}}x_{n-i_0}x_{n-i_1}\cdots x_{n-i_{2j-1}} c f(x_{n-i_0}, x_{n-i_1}, \ldots, x_{n-i_{2k}})},$$ and $$x_{n 1}={c\sum\limits_{j=1}^{k}\sum\limits_{( i_0, i_1,\ldots, i_{2j-1})\in A_{2j-1}}x_{n-i_0}x_{n-i_1}\cdots x_{n-i_{2j-1}} c f(x_{n-i_0}, x_{n-i_1}, \ldots, x_{n-i_{2k}})\over c\sum\limits_{j=0}^{k}\sum\limits_{( i_0, i_1,\ldots, i_{2j})\in A_{2j}}x_{n-i_0}x_{n-i_1}\cdots x_{n-i_{2j}} f(x_{n-i_0}, x_{n-i_1}, \ldots, x_{n-i_{2k}})}.$$ We prove that their unique positive equilibrium $\overline{x} =1$ is globally asymptotically stable. And a new access is presented to study the theory of recursive sequences. |
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