一个化学反应系统的全局结构

Global behavior of solution of a chemical reaction system

文中考虑一个自催化反应的数学模型ｄｘｄｔ＝－ａ１ｘ－ａ２ｘ２＋ａ３ｘｙ＋ａ４ｘ２ｙ；ｄｙｄｔ＝ａ０＋ａ２ｘ２－ａ３ｘｙ－ａ４ｘ２ｙ（ａ０，ａ１＞０，ａ２，ａ３，ａ４≥０），先给出ａ３ａ１＋ａ０ａ４ａ２１２≥ａ４ａ１－ａ２ａ３ａ２１时解的性态，然后结合已知的结果完整地给出了此系统解的全局性态。文中还指正了井竹君等一文的一个错误。

For the reaction system of chemical and biochemical interest: [JB({〗 d x d t=-a 1x-a 2x 2+a 3xy+a 4x 2y d y d t=a 0+a 2x 2-a 3xy-a 4x 2y(a 0,a 1>0, a 2, a 3, a 4≥0) global behavior of the solutions is shown as a 3a 1+a 0a 4a 1 2 2≥a 4a 1-a 2a 3a 1 2 . Combining this result with the known results, the global structure of the system for any practical case is obtained. In addition, an error in the paper by Jing Zhu jun and Chen Lan sun (1983) is pointed out and corrected.