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首页> 外文期刊>NanoBioscience, IEEE Transactions on >Stability and Bifurcation Analysis of Models for Zebrafish Somitogenesis
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Stability and Bifurcation Analysis of Models for Zebrafish Somitogenesis

机译：斑马鱼体发生模型的稳定性和分叉分析

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摘要

Notch-Delta signaling is indispensable for somitogenesis, which controls the vertebrate segmentation during embryonic development. Several theoretical models have been proposed to explain this interesting process. In zebrafish somitogenesis, genes her1, her7, delta, and their proteins plays the important roles. However, an auto-repression model with time delay involved only by her1/her7 is able to explain zebrafish somitogenesis. This paper will systematically study the dynamics of this model. Specifically we investigate its stability, bifurcation (oscillation), and stability of oscillation. First, the conditions for both stability and bifurcation are presented based on the linearized model. Then three indices for bifurcation of this nonlinear model are derived by using linear functional operator analysis. Finally, the numerical simulations are carried out to illustrate the theoretical results developed in this study.
机译：Notch-Delta信号对于体发生是必不可少的，这种体发生在胚胎发育过程中控制着脊椎动物的分化。已经提出了几种理论模型来解释这个有趣的过程。在斑马鱼的体细胞发生中，基因her1，her7，delta及其蛋白起着重要的作用。然而，仅由her1 / her7参与的具有时间延迟的自动抑制模型能够解释斑马鱼的体细胞发生。本文将系统地研究该模型的动力学。具体来说，我们研究其稳定性，分叉（振荡）和振荡稳定性。首先，基于线性化模型给出了稳定性和分支的条件。然后，通过线性函数算子分析得出了该非线性模型的三个分叉指标。最后，进行了数值模拟，以说明本研究开发的理论结果。

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