本文選題：遺傳撥動開關(guān)　切入點：Poincaré-Bendixson定理　出處：《四川大學學報(自然科學版)》2017年04期

【摘要】：本文研究一個具有協(xié)同數(shù)為1的遺傳撥動開關(guān)系統(tǒng)的全局定性性質(zhì).本文首先證明該系統(tǒng)僅有一個平衡點且為穩(wěn)定結(jié)點,再利用Poincaré-Bendixson定理證明系統(tǒng)沒有周期軌,最后證明系統(tǒng)恰有兩個無窮遠平衡點且均為鞍結(jié)點,從而獲得系統(tǒng)的全局定性結(jié)構(gòu),并由此知系統(tǒng)是全局單穩(wěn)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.
【作者單位】： 四川大學數(shù)學學院;
【基金】：國家自然科學基金(11461228)
【分類號】：O175
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本文編號：1671692