Spatially Nonhomogeneous Hopf and Turing Bifurcations Driven by the Nonlocal Effect With the Spatial Average Kernel

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-28 DOI:10.1002/mma.10730

Shuyang Xue, Yongli Song

引用次数: 0

Abstract

In this paper, we first derive the algorithm of calculating the normal form of spatially nonhomogeneous Hopf bifurcation and Turing bifurcation for the general reaction–diffusion system with spatial average. Then we investigate the spatiotemporal dynamics of nonlocal Lotka–Volterra competitive model and nonlocal Holling–Tanner predator–prey model. It has been shown that the spatial average is a new mechanism to induce the patterns. By calculating the normal form, the type of bifurcation and stability of spatiotemporal patterns bifurcating from the constant equilibrium are investigated. For the nonlocal Lotka–Volterra competitive model, the coexistence of two spatially nonhomogeneous spatial patterns is found. For the nonlocal Holling–Tanner predator–prey model, we found not only the coexistence of two spatially nonhomogeneous spatial patterns but also the stable spatially nonhomogeneous periodic patterns.

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空间平均核非局部效应驱动的空间非齐次Hopf分岔和图灵分岔

本文首先推导了具有空间平均的一般反应扩散系统的空间非齐次Hopf分岔和图灵分岔范式的计算算法。然后研究了非局部Lotka-Volterra竞争模型和非局部Holling-Tanner捕食者-猎物模型的时空动态。研究表明，空间平均是一种新的诱导模式的机制。通过范式的计算，研究了从恒定平衡出发的时空格局的分岔类型和稳定性。对于非局部Lotka-Volterra竞争模型，发现两种空间非均匀的空间格局共存。对于非局部Holling-Tanner捕食者-猎物模型，我们不仅发现了两种空间非均匀的空间模式共存，而且发现了稳定的空间非均匀周期模式。

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.