遗传拨动开关系统的全局稳定性

发布时间：2018-03-27 13:24

  本文选题：遗传拨动开关　切入点：Poincaré-Bendixson定理　出处：《四川大学学报(自然科学版)》2017年04期

【摘要】：本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.本文首先证明该系统仅有一个平衡点且为稳定结点,再利用Poincaré-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,并由此知系统是全局单稳的.
[Abstract]:In this paper, we study the global qualitative properties of a genetic toggle switch system with a synergistic number of 1. In this paper, we first prove that the system has only one equilibrium point and is a stable node, and then, by using Poincar 茅 -Bendixson theorem, we prove that the system has no periodic orbit. Finally, it is proved that the system has exactly two infinite equilibrium points and both of them are saddle nodes, thus the global qualitative structure of the system is obtained, and the global Monostability of the system is obtained.
【作者单位】： 四川大学数学学院;
【基金】：国家自然科学基金(11461228)
【分类号】：O175
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本文编号：1671692