一个遗传拨动开关系统的全局稳定性

Global monostability of a genetic toggle switch system

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.

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.