| 一类有理差分方程解的全局行为 |
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| 引用本文： | 骆元媛,张倩.一类有理差分方程解的全局行为[J].四川大学学报(自然科学版),2012,49(6):1214-1218. |
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| 作者姓名： | 骆元媛 张倩 |
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| 作者单位： | 1. 四川大学数学学院,成都,610064
2. 西南科技大学理学院,绵阳,621010 |
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| 摘 要： | 本文讨论了一个带有参数的分子含有二次项的有理差分方程的奇点集和解的全局稳定性,证明了它的解由于参数的取值不同最终将收敛到0或非零不动点或二周期点或者是无界的,且在某些情况下解的收敛性还依赖于给定的初始值,从而回答了Sedaghat提出的一个公开问题.
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| 关 键 词： | 差分方程 全局行为 奇点集 |
| 收稿时间： | 2011/7/19 0:00:00 |
Global behavior of a rational difference equation |
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| LUO Yuan-Yuan and ZHANG Qian.Global behavior of a rational difference equation[J].Journal of Sichuan University (Natural Science Edition),2012,49(6):1214-1218. |
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| Authors: | LUO Yuan-Yuan and ZHANG Qian |
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| Institution: | College of Mathematics, Sichuan University;College of Mathematics, Sichuan University |
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| Abstract: | In this paper,the authors discuss the global behavior of a rational difference equation with parameters and a quadratic numerator.The forbidden set is obtained and it is showed that for all initial values outside the forbidden set,its solutions may converge to 0,or to a nonzero fixed point,or they may be periodic of period 2 or unbounded according to different values of parameters.In some cases,different types of solutions coexist depending on the initial values.The work answers an open problem proposed by Sedaghat. |
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| Keywords: | difference equation global behavior forbidden set |
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