细胞再生模型的数值模拟和定性分析

针对一个组织被切割后如何再生的问题，对活化质-抑制剂模型描述的细胞再生模型，应用交替方向隐格式方法，进行了数值模拟，画出了模型三维图像，并用李雅普诺夫-施密特方法对它的平衡点作了分析。结果表明，在一定的参数范围内，该平衡点为超临界分岔点，也为鞍-结分岔点。这表示参数经过一个临界值后，由原来再生一个细胞变成再生两个细胞。

Numerical Simulation and Qualitative Analysis of a Cell Regeneration Model

To solve the regeneration of an organization having been cut, the pattern of a cell regeneration model, which is described by activator inhibitor model, were obtained by numerical simulation, using Alternative Direction Implicit(ADI) form, and its 3 D figures were drawn. The critical points were qualitatively analysed using Liapunov Schmidt method. The results show that it is a supercritical bifurcation point, or saddle node bifurcation point under some parameters ranges. It shows that the cell regeneration is from one to two as the parameter varies through the critical value.