| 两类耦合竞争系统平衡点稳定性 |
| Alternative Title | The stability of equilibrium of the two types of coupling competitive system
|
| 牛林 |
| Thesis Advisor | 林国
|
| 2013-05-23
|
| Degree Grantor | 兰州大学
|
| Place of Conferral | 兰州
|
| Degree Name | 学士
|
| Keyword | 不动点
压缩矩形
渐近稳定
|
| Abstract | 在动力系统及其应用中，不动点的研究扮演了重要的角色。然而，为了保证一个不动点有物理（生物，化学，甚至经济）意义，必须满足一定的稳定性假设。即一个不动点称为稳定的，如果附近的解在将来都仍然逗留在附近。
本文首先使用一种已被定义的压缩矩形，证明一个压缩矩形与渐近稳定点之间关系的定理，再在某一类的不动点附近构造相应的压缩矩形，运用得到的定理，判断该不动点的稳定性。并通过两个具体的例子，运用多元函数在有限区间上求最值的方法，找出系统正常状态的充分条件。 |
| Other Abstract | In this paper,we use a defintion of a contracting rectangle at first.Then we give a theorem about the relationship between the contracting rectangle and the point which is asymptotically stable.After that,we define the contracting rectangle about some fixed points.Using the theorem ,we can estimate the stability of the point.Then in a specific system ,we use the method which is used to solve the maximum and the minimum of the function of several variables in some regions to find some sufficient condition of the positive steady state of the system. |
| URL | 查看原文
|
| Language | 中文
|
| Document Type | 学位论文
|
| Identifier | https://ir.lzu.edu.cn/handle/262010/224888
|
| Collection | 数学与统计学院
|
Recommended Citation
GB/T 7714 |
牛林. 两类耦合竞争系统平衡点稳定性[D]. 兰州. 兰州大学,2013.
|
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
