二次自催化反应系统无极限环的条件

本文的结论是,当自催化反应中的微分方程组(1)在A~2≥B时不存在极限环,且唯一平衡点在右半平面内是渐近稳定的。关键词:自催化,反应系统,极限环。

Conditon that the Reaction System with Second—Order Autocatalysis Has no Limit Cycle

In this paper we consider the reaction system of chemical and bioche-mical interest: dx/dt=-a_1x-a_2x~2+a_3xy +a_4x~2y dy/dt=a_0+a_2x_2-a_3xy-a_4x~2ywhere a_0 is a positive constant, a_1, a_2, a_3, and a_4 are nonnegative react-ion constants Paper [2] proved that there is a unique limit cycle under the conditionB>A~2. In this paper the following results are obtained. If B≤A~2, then equation (1) has no limit cycle, and the equilibrium pointis asymptotically stable in half plane X>0, where A = a_3/a_1+a_0a_4/a_1~2, B =a_4/a_1-a_2a_3/a_1~2