| 一个遗传拨动开关系统的全局稳定性 |
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| 引用本文： | 李洁,何志蓉. 一个遗传拨动开关系统的全局稳定性[J]. 四川大学学报(自然科学版), 2017, 54(4): 675-678 |
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| 作者姓名： | 李洁 何志蓉 |
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| 作者单位： | 四川大学数学学院,四川大学 |
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| 摘 要： | 该文研究一个具有协同数为1的遗传拨动开关系统的全局定性性质. 首先证明该系统仅有一个平衡点且为稳定结点, 再利用Poincare-Bendixson 定理证明系统没有周期轨, 最后证明系统恰有两个无穷远平衡点且均为鞍结点, 从而获得系统的全局定性结构, 由此知系统是全局单稳的.
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| 关 键 词： | 遗传拨动开关；Poincare-Bendixson 定理； 周期轨；Poincare 变换； 无穷远平衡点 |
| 收稿时间： | 2016-10-15 |
| 修稿时间： | 2017-01-02 |
Global monostability of a genetic toggle switch system |
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| LI Jie and HE Zhong-Rong. Global monostability of a genetic toggle switch system[J]. Journal of Sichuan University (Natural Science Edition), 2017, 54(4): 675-678 |
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| Authors: | LI Jie and HE Zhong-Rong |
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| Affiliation: | Sichuan University |
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| Abstract: | In this paper the global qualitative properties of a system which models a genetic toggle switch with cooperativties $1$ are given. Firstly it is proved that the system has a unique equilibrium, which is a stable node. Then it is shown that there are no periodic orbits by the Poincare-Bendixson Theorem, and the system has exactly two equilibria at infinity, which are both saddle-nodes. Consequently, the global phase portrait indicates the system is globally monostable. |
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| Keywords: | genetic toggle switch Poincare-Bendixson Theorem periodic orbit Poincare transformation equilibria at infinity |
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