关于颞部骨块形成模型的极限环问题

Limit Cycles in a Temporal Morphogenesis Model

考虑颞部骨块形态形成过程中抑制度的变化不仅与激活度的平方成正比,而且与激活度本身的浓度成正比,对Gierer-Meinhardt给出的颞部骨块形态形成过程的基本模型进行改进,利用常微分方程定性理论研究了颞部骨块的形态形成模型平衡点的性态,并得到该系统的极限环的存在性和极限环的唯一性的条件。

In this paper, we consider a temporal morphogenesis model which is a generalization of the model studied by Gierer-Meinhardt. In the model, we assume that the inhibitor concentration is not only proportional to the square of the concentration of the activator but also to the one of activator itself. Using the theory of qualitative analysis of ordinary differential equation, the properties of the equilibrium points, the existence and uniqueness of limit cycles in a temporal morphogenetic model are obtained.