Analysis of an improved fractional-order model of boundary formation in the Drosophila large intestine dependent on Delta-Notch pathway.

IF 4.1 3区数学 Q1 Mathematics Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-07-23 DOI:10.1186/s13662-020-02836-1

Deshun Sun, Lingyun Lu, Fei Liu, Li Duan, Daping Wang, Jianyi Xiong

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引用次数: 3

Abstract

In this paper, an improved fractional-order model of boundary formation in the Drosophila large intestine dependent on Delta-Notch pathway is proposed for the first time. The uniqueness, nonnegativity, and boundedness of solutions are studied. In a two cells model, there are two equilibriums (no-expression of Delta and normal expression of Delta). Local asymptotic stability is proved for both cases. Stability analysis shows that the orders of the fractional-order differential equation model can significantly affect the equilibriums in the two cells model. Numerical simulations are presented to illustrate the conclusions. Next, the sensitivity of model parameters is calculated, and the calculation results show that different parameters have different sensitivities. The most and least sensitive parameters in the two cells model and the 60 cells model are verified by numerical simulations. What is more, we compare the fractional-order model with the integer-order model by simulations, and the results show that the orders can significantly affect the dynamic and the phenotypes.

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依赖于Delta-Notch通路的果蝇大肠边界形成改进分数阶模型的分析。

本文首次提出了一种改进的依赖于Delta-Notch通路的果蝇大肠边界形成的分数阶模型。研究了解的唯一性、非负性和有界性。在双细胞模型中，存在两种平衡(Delta的无表达和Delta的正常表达)。证明了这两种情况的局部渐近稳定性。稳定性分析表明，分数阶微分方程模型的阶数对两单元模型的平衡有显著影响。通过数值模拟来验证本文的结论。其次，对模型参数的灵敏度进行了计算，计算结果表明，不同的参数具有不同的灵敏度。通过数值模拟验证了两单元模型和60单元模型的最敏感参数和最不敏感参数。通过对分数阶模型和整数阶模型的模拟比较，结果表明，分数阶对动态和表型有显著影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Difference Equations 数学-数学

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审稿时长

4-8 weeks

期刊介绍： The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.