Pattern Formation of Nonconstant Steady-State Solutions to the n-Dimensional Glycolysis Model
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摘要: 研究了一类带Neumann边界条件的n维糖酵解模型.首先,以扩散系数d1为分歧参数,运用局部分歧理论分析了该模型非常数稳态解的局部结构.其次,利用全局分歧理论和Leray-Schauder度理论讨论了非常数稳态解的全局存在性.最后,借助数值模拟证实了所得结论.分析结果表明n维糖酵解模型的空间模式可以生成.Abstract: A glycolysis model under the Neumann boundary condition was investigated in the n-dimensional space. Based on the local bifurcation theory, the local structure of the nonconstant steady-state solution to the model was studied with diffusion coefficient d1 as the bifurcation parameter. Then, according to the global bifurcation theory and the Leray-Schauder degree theory, global existence of the nonconstant steady-state solution was discussed. Moreover, the theoretical results were confirmed through numerical simulations. It is shown that the spatial pattern can form for the glycolysis model.
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Key words:
- glycolysis model /
- steady-state solution /
- pattern formation /
- global bifurcation
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