余维1全局分岔引起的真菌顶端生长
Fungal tip growth arising through a codimension-1 global bifurcation
摘要：
顶端生长是真菌细胞中发生的生长阶段。在尖端生长过程中，细胞表现出连续的极端纵向生长，而其形状在质量上保持不变。单细胞真菌顶端生长的模型由弹道老化薄粘性片（BATS）模型给出，该模型由一阶微分方程的5维系统组成。BATS模型的解决方案，对应于真菌的尖端生长出现通过余维1全局分歧的2参数的解决方案。在本文中，我们推导出一个玩具模型的BATS模型。玩具模型由依赖于单个参数的一阶微分方程的2维系统给出。本文的主要成果是证明了玩具模型具有BATS模型的余维1全局分支。证明的一个重要组成部分是一个拓扑方法，使识别的歧点。最后，我们讨论了如何证明可以推广到BATS模型。
英文摘要：
Tip growth is a growth stage which occurs in fungal cells. During tip growth, the cell exhibits continuous extreme lengthwise growth while its shape remains qualitatively the same. A model for single celled fungal tip growth is given by the Ballistic Ageing Thin viscous Sheet (BATS) model, which consists of a 5-dimensional system of first order differential equations. The solutions of the BATS model that correspond to fungal tip growth arise through a codimension-1 global bifurcation in a 2-parameter family of solutions. In this paper we derive a toy model from the BATS model. The toy model is given by 2-dimensional system of first order differential equations which depend on a single parameter. The main achievement of this paper is a proof that the toy model exhibits an analogue of the codimension-1 global bifurcation in the BATS model. An important ingredient of the proof is a topological method which enables the identification of the bifurcation points. Finally, we discuss how the proof may be generalized to the BATS model.
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