CMMSE: New Properties of Auto-Wave Solutions in Activator-Inhibitor Reaction-Diffusion Systems With Fractional Derivatives

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-12-23 DOI:10.1002/mma.10672

Bohdan Datsko, Vasyl Gafiychuk

引用次数: 0

Abstract

In this article, we analyze new properties of auto-wave solutions in fractional reaction-diffusion systems. These new properties arise due to a change in fractional derivative order and do not occur in systems with classical derivatives. It is shown that the stability of steady-state solutions and their evolution are mainly determined by the eigenvalue spectrum of a linearized system and the fractional derivative order. It is also demonstrated that the basic properties of auto-wave solutions in fractional-order systems can essentially differ from those in standard systems. The results of the linear stability analysis are confirmed by computer simulations of the generalized fractional van der Pol–FitzHugh–Nagumo mathematical model. A common picture of possible instabilities and auto-wave solutions in time-fractional two-component activator-inhibitor systems is presented.

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分数阶导数活化剂-抑制剂反应-扩散体系中自波解的新性质

本文分析了分数阶反应扩散系统中自波解的新性质。这些新的性质是由于分数阶导数顺序的改变而产生的，在具有经典导数的系统中不会发生。结果表明，稳态解的稳定性及其演化主要由线性化系统的特征值谱和分数阶导数阶数决定。还证明了分数阶系统中自波解的基本性质与标准系统中的基本性质有本质的区别。通过对广义分数阶van der Pol-FitzHugh-Nagumo数学模型的计算机模拟，验证了线性稳定性分析的结果。给出了时间分数双组分活化剂-抑制剂系统可能的不稳定性和自波解的一般情况。

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

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.