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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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.