遗传拨动开关系统的全局稳定性

摘要

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 Poincaré-Bendixson Theorem,and the system has exactly two equilibria at infinity,which are both saddle-nodes.Consequently,the global phase portrait indicates that the system is globally monostable.%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.