数学学报    2011 54 (4): 553-560   ISSN: 0583-1431  CN: 11-2039/O1   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 收稿日期 2008-06-02  修回日期 2010-12-07  网络版发布日期 2011-07-15 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. 通讯作者: 吴建华