Bifurcation Analysis of a Calcium Oscillation Model
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 (2015) 一个钙振荡模型的分支分析。 应用数学进展， 4， 7-14. doi: 10.12677/AAM.2015.41002
 Cuthbertson, K.S.R. and Chay, T.R. (1991) Modelling receptor-controlled intracellular calcium oscillators. Cell Calcium, 12, 97-109.
 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.
 Wiggins, S. (1990) Introduction to applied nonlinear dynamical systems and chaos. Springer, Berlin.