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.
Similar content being viewed by others
References
Chen Lan-sun,Theory and Methods on Mathecology, Academic Press, Beijing (1988). (in Chinese)
Zhou Jian-ying, Zhang Jin-yan and Zeng Xian-wu, A qualitative analysis for a kind of nonlinear equations concerning biochemical recreation,Acta Math. Appl. Sinica,5, 3 (1982), 234–240. (in Chinese)
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)
Zhang Jin-yan,Geometric Theory for Ordinary Differential Equations and Problems of Its Bifurcations, Peking Univ. Press, Beijing (1981), (in Chinese)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wei-nian, Z. Existence of closed orbits for a differential equation model concerning multi-molecule reactions. Appl Math Mech 14, 589–596 (1993). https://doi.org/10.1007/BF02451369
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02451369