...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Wireless personal communications: An Internaional Journal >Bifurcation Analysis About a Mathematical Model of Somitogenesis Based on the Runge–Kutta Method
【24h】

Bifurcation Analysis About a Mathematical Model of Somitogenesis Based on the Runge–Kutta Method

机译：基于跳动-Kutta方法的生物生成数学模型的分岔分析

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

In this paper, we investigated the modified two dimensional model which can explain somite patterning in embryos. It is suitable for exploring a design space of somitogenesis and can explain aspects of somitogenesis that previous models cannot. Here, we mainly studied the non-diffusing case. We have used the Hopf bifurcation theorem, the Center manifold theorem and Runge–Kutta method in our investigation. First, we investigate its dynamical behaviors and put forward a sufficient condition for the oscillation of the small network. Then, we give the mathematical simulation based on the Runge–Kutta method. In the process of solving ordinary differential equations, the four order Runge–Kutta method has the advantages of high accuracy, convergence and stability (under certain conditions), which can change the step size and do not need to calculate higher order derivatives. Therefore, it has become the most commonly used numerical solution. At the same time, we get the sufficient condition in which the bistable state of the system exists and give the numerical simulation. Because somitogenesis occupies an important position in the process of biological development, and as a pattern process can be used to study pattern formation and many aspects of embryogenesis. So our study have a great help for embryonic development, gene expression, cell differentiation. In addition, it is beneficial to study the clone animal variation problem of spinal bone number and is of great help to the treatment and prevention of defects of human spine disease.
机译：在本文中，我们调查了改进的二维模型，可以在胚胎中解释一人的图案化。它适用于探索同化体的设计空间，可以解释先前模型不能的同化体的方面。在这里，我们主要研究了非漫射案例。我们在调查中使用了Hopf Bifurcation定理，中心歧管定理和跳动 - 库特拉方法。首先，我们调查其动态行为，并提出了足够的条件来振荡小型网络。然后，我们基于runge-kutta方法给出数学仿真。在求解常微分方程的过程中，四阶runge-kutta方法具有高精度，收敛和稳定性（在某些条件下）的优点，这可以改变步长，不需要计算更高阶的衍生物。因此，它已成为最常用的数值解决方案。同时，我们获得了系统的双稳态状态存在并提供数值模拟的充分状态。因为Somitogenesis占据生物发育过程中的重要地位，并且作为模式过程可用于研究模式形成和胚胎发生的许多方面。因此，我们的研究对胚胎发育，基因表达，细胞分化具有很大的帮助。此外，研究脊柱骨数的克隆动物变异问题是有益的，对人脊椎病的缺陷有很大的帮助。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号