Existence of Closed Orbits for a Differential Equation Model Concerning Multi-Molecule Reactions

Zhang Wei-nian

Volume 14 Issue 6

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Article Navigation > Applied Mathematics and Mechanics > 1993 > 14(6): 559-566

Zhang Wei-nian. Existence of Closed Orbits for a Differential Equation Model Concerning Multi-Molecule Reactions[J]. Applied Mathematics and Mechanics, 1993, 14(6): 559-566.

Citation:

Zhang Wei-nian. Existence of Closed Orbits for a Differential Equation Model Concerning Multi-Molecule Reactions[J]. Applied Mathematics and Mechanics, 1993, 14(6): 559-566.

Citation:

Zhang Wei-nian. Existence of Closed Orbits for a Differential Equation Model Concerning Multi-Molecule Reactions[J]. Applied Mathematics and Mechanics, 1993, 14(6): 559-566.

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Existence of Closed Orbits for a Differential Equation Model Concerning Multi-Molecule Reactions

Zhang Wei-nian

Centre for Mathematical Sciences, Chengdu Institute of Computer Applications, Academia Sinica, Chengdu

Received Date: 1992-05-30
Publish Date: 1993-06-15

Abstract

Abstract

In this paper, the existence of closed orbits for the biochemical reaction model dx/dt=1-xⁿy²,dy/dt=a(xⁿy²-y) is discussed, where n is a positive integer and x≥0,y≥0,a>0 We also point out that the equation has no dosed orbits or has stable limit cycles arising from Hopf bifurcations under a certain condition of a.
- closed orbit,
- limit cycle,
- fine focus,
- Hopf bifurcation

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References(4)

References

[1]	陈兰荪,《数学生态学的理论和方法》,科学出版社〔1988).
[2]	周建莹、张锦炎、曾宪武,生化反应中一类非线性方程的定性分析,应用数学学报,5(3)(1982),234-240.
[3]	李嘉旭、范弘毅、姜天来、陈秀东,一类多分子反应微分方程模型的定性分析,生物数学学报,5(2)(1990),182-170.
[4]	张锦炎,《常微分方程几何理论与分支问题》,北京大学出版社(1981).