| Autor: |
de Jong, T. G., Sterk, A. E., Broer, H. W. |
| Rok vydání: |
2019 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| DOI: |
10.1142/S0218127420501072 |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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