一类生化反应微分方程的定性分析

Qualitative analysis of a kind of differential equation of biochemical reaction

对一类生化反应模型x=δ-ax-xpyq,y=xpyq-by(δ>0,b>0,a>0,p 1,q>1)进行了研究.讨论了系统平衡点的稳定性态,对系统极限环的位置做出了估计.同时讨论了系统无环的充分条件以及极限环存在惟一性条件.

In this paper, a kind of biochemical model =δ-ax-x^py^q,=x^py^q-by(δ>0,b>0,a>0,p1,q>1) is studied. The stability of equilibrium is discussed. The location of the limit cycle of this system is estimated. Meanwhile, the sufficient conditions of nonexistence and the conditions of existence and uniqueness of the limit cycle of the model in the first quadrant are discussed.