具有交叉扩散和非局部延迟的水-植被模型中的模式动力学

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-12 DOI:10.1002/mma.10480

Gaihui Guo, Jing You, Khalid Ahmed Abbakar

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引用次数: 0

摘要

在半干旱地区，植被和土壤水分的正反馈效应在植物根系的吸水过程中发挥着不可或缺的作用。此外，植被还能通过根系的非局部相互作用吸收水分。因此，本文考虑了交叉扩散和非局部延迟之间的相互作用如何影响植被生长。通过数学分析，得到了水-植被模型中图灵模式出现的条件。同时，利用多尺度分析方法，得到了图灵分岔边界附近的振幅方程。通过分析振幅方程的稳定性，确定了条纹、六边形、条纹与六边形混合等图灵图案出现的条件。为说明分析结果，特别是不同参数下植被图案的演变过程，给出了一些数值模拟。

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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Pattern dynamics in a water–vegetation model with cross‐diffusion and nonlocal delay

In semiarid areas, the positive feedback effect of vegetation and soil moisture plays an indispensable role in the water absorption process of plant roots. In addition, vegetation can absorb water through the nonlocal interaction of roots. Therefore, in this article, we consider how the interactions between cross‐diffusion and nonlocal delay affect vegetation growth. Through mathematical analysis, the conditions for the occurrence of the Turing pattern in the water–vegetation model are obtained. Meanwhile, using the multi‐scale analysis method, the amplitude equation near the Turing bifurcation boundary is obtained. By analyzing the stability of the amplitude equation, the conditions for the appearance of Turing patterns such as stripes, hexagons, and mixtures of stripes and hexagons are determined. Some numerical simulations are given to illustrate the analytical results, especially the evolution processes of vegetation patterns depicted under different parameters.

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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.