数学学报 2011, 54(4) 553-560 DOI:      ISSN: 0583-1431 CN: 11-2038/O1

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本文关键词相关文章
糖酵解模型
平衡解
先验估计
本文作者相关文章
一类糖酵解模型正平衡解的存在性分析
魏美华, 吴建华
陕西师范大学数学与信息科学学院 西安 710062
摘要: 研究生化反应中具有代表性的一类糖酵解模型. 运用先验估计讨论非常数正平衡解的不存在性, 得到非常数正平衡解存在的必要条件. 在常数平衡解Turing不稳定的基础上, 利用度理论方法和解的先验估计,进一步给出非常数正平衡解存在的充分条件.  
关键词 糖酵解模型   平衡解   先验估计  
MSC2000 O175.26
Existence Analysis of the Positive Steady-State Solutions for a Glycolysis Model
Mei Hua WEI, Jian Hua WU
College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, P. R. China
Abstract: This paper deals with a representative glycolysis model in biochemical reaction. We study the non-existence of non-constant positive steady-state solutions by using a priori estimates. A necessary condition for the existence of non-constant positive steady-state solutions is obtained. On the basis of Turing instability of constant steady-state solutions, the degree theory is combined with a priori estimates to give a sufficient condition for the existence of non-constant positive steady-state solutions.  
Keywords: glycolysis model   steady-state solutions   a priori estimates  
收稿日期 2008-06-02 修回日期 2010-12-07 网络版发布日期  
DOI:
基金项目:

国家自然科学基金资助项目(10971124);教育部高等学校博士点专项基金资助项目(200807180004)

通讯作者: 吴建华
作者简介:
作者Email: jianhuaw@snnu.edu.cn

参考文献:
[1] Higgins J., A chemical mechanism for oscillations of glycolytic intermediates in yeast cells, Proc. Natl. Acad. Sci. USA, 1964, 51(6): 989-994.

[2] Bhargava S. C., On the higgins model of glycolysis, Bull. Math. Biol., 1980, 42(6): 829-836.

[3] Peng R., Shi J. P., Wang M. X., On stationary pattern of a reaction-diffusion model with autocatalysis and saturation law, Nonlinearity, 2008, 21(7): 1471-1488.

[4] Sel’kov E. E., Self-oscillations in glycolysis, Eur. J. Biochem., 1968, 4(1): 79-86.

[5] Davidson F. A., Rynne B. P., A priori bounds and global existence of solutions of the steady-state Sel’kov model, Proc. Roy. Soc. Edinburgh Sect. A, 2000, 130(3): 507-516.

[6] Peng R., Qualitative analysis of steady states to the Sel’kov model, J. Differential Equations, 2007, 241(2): 386-398.

[7] Ashkenazi M., Othmer H. G., Spatial patterns in coupled biochemical oscillators, J. Math. Biol., 1978, 5(4): 305-350.

[8] Segel L. A., Mathematical Models in Molecular and Cellular Biology, Cambridge: Cambridge University Press, 1980.

[9] Goldbeter A., Nicolis G., An allosteric enzyme model with positive feedback applied to glycolytic oscillations, Prog. Theor. Biol., 1976, 4: 65-160.

[10] Othmer H. G., Aldridge J. A., The effects of cell density and metabolite flux on cellular dynamics, J. Math. Biol., 1978, 5(2): 169-200.

[11] Lou Y., Ni W. M., Diffusion, self-diffusion and cross-diffusion, J. Differential Equations, 1996, 131(1): 79- 131.

[12] Li Y. L., Li H. X., Wu J. H., Coexistence states of the unstirred chemostat model, Acta Mathematica Sinica, Chinese Series, 2009, 52(1): 141-152.

[13] Wu J. H., Global bifurcation of coexistence state for the competition model in the chemostat, Nonlinear Anal., 2000, 39(6): 817-835.
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