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Applied Mathematics and Mechanics

, Volume 14, Issue 6, pp 589–596 | Cite as

Existence of closed orbits for a differential equation model concerning multi-molecule reactions

  • Zhang Wei-nian
Article

Abstract

In this paper, the existence of closed orbits for the biochemical reaction model\(i\dot a = \hat H(t)a\) is discussed, where n is a positive integer and x≥0, y≥0, a>0. We also point out that the equation has no closed orbits or has stable limit cycles arising from Hopf bifurcations under a certain condition of a.

Key words

closed orbit limit cycle fine focus Hopf bifurcation 

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References

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    Chen Lan-sun,Theory and Methods on Mathecology, Academic Press, Beijing (1988). (in Chinese)Google Scholar
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    Li Jia-xu, Fan Hong-yi, Jiang Tian-lai and Chen Xiu-dong, A qualitative analysis for a kind of differential equation models concerning multi-molecule recreation,J. Biomath. 5, 2 (1990), 162–170. (in Chinese)MathSciNetGoogle Scholar
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    Zhang Jin-yan,Geometric Theory for Ordinary Differential Equations and Problems of Its Bifurcations, Peking Univ. Press, Beijing (1981), (in Chinese)Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1993

Authors and Affiliations

  • Zhang Wei-nian
    • 1
  1. 1.Centre for Mathematical Sciences, Chengdu Institute of Computer ApplicationsAcademia SinicaChengdu

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