细胞钙振荡模型的Hopf分岔与计算机仿真

Hopf Bifurcation Analysis and Computer Simulation of Cell Calcium Oscillation Model

利用中心流形定理和分岔理论,研究了Borghans-Dupont模型平衡点分岔现象,揭示了钙振荡现象发生机理。通过对系统分岔现象的理论分析,不仅证明了Hopf分岔的存在,而且也说明了振荡现象产生和消失的主要原因来源于两个分别为超临界和亚临界的Hopf分岔。利用计算机仿真,绘制了系统平衡点分岔图、相图与时序图,验证了理论分析的正确性。

The bifurcation mechanisms of the Borghans-Dupont model of calcium oscillation were investigated. By apply- ing the centre manifold and bifurcation theory, a theoretical analysis of bifurcation in this model was first performed. The results not only exhibite the Hopf bifurcation but also show that the supercritical Hopf bifurcation and the subcriti- cal Hopf bifurcation play a great role in the calcium oscillations. Our computer simulations, including the bifurcation dia- gram of fixed points, the bifurcation diagram of the system in two dimensional parameter space and time series, have been plotted in order to illustrate the correctness of the theoretical and dynamical analysis.