一个钙振荡模型的分支分析
Bifurcation Analysis of a Calcium Oscillation Model
DOI: 10.12677/AAM.2015.41002,
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作者:
申屠旻, 常 玉：北京化工大学理学院，数学系，北京
关键词:
分支；中心流形；钙振荡；Bifurcation； The Center Manifold； Calcium Oscillation
摘要:
本文应用中心流形定理和分支理论研究了一个钙振荡模型的分支现象。从理论上严格分析了钙振荡模型中的Hopf分支的存在性。数值分析结果表明钙振荡模型中的拟周期振荡现象的产生是由环面分支引起的。此外，通过数值模拟，我们也发现了一些和之前研究结果不同的新的复杂动态，例如环面分支和cyclic fold分支。
Abstract: The bifurcation of a calcium oscillation model is investigated by applying the center manifold theorem and the bifurcation theory. We theoretically analyze the existence of Hopf bifurcation. The numerical analysis results suggest that the quasi-periodic oscillation in this model results from torus bifurcation. Numerical simulation also shows some new complex dynamics, such as torus bifurcation and cyclic fold bifurcation which are different from the results before.
文章引用:
申屠旻, 常玉. 一个钙振荡模型的分支分析[J]. 应用数学进展, 2015, 4(1): 7-14. http://dx.doi.org/10.12677/AAM.2015.41002
参考文献
|
[1]
|
Cuthbertson, K.S.R. and Chay, T.R. (1991) Modelling receptor-controlled intracellular calcium oscillators. Cell Calcium, 12, 97-109.
|
|
[2]
|
Wang, J.H., Huang, X.D. and Huang, W.D. (2007) A quantitative kinetic model for ATP-induced intracellular Ca2+ oscillations. Journal of Theoretical Biology, 245, 510-519.
|
|
[3]
|
Wiggins, S. (1990) Introduction to applied nonlinear dynamical systems and chaos. Springer, Berlin.
|