Spatio-temporal patterns and global bifurcation of a nonlinear cross-diffusion predator–prey model with prey-taxis and double Beddington–DeAngelis functional responses

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Demou Luo , Qiru Wang
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引用次数: 0

Abstract

The aim of this article is investigating the spatio-temporal patterns of a nonlinear cross-diffusion predator–prey model with prey-taxis and double Beddington–DeAngelis functional responses. First, by utilizing user-friendly version of Crandall–Rabinowitz bifurcation theory as an analytical method, the spatio-temporal patterns of positive steady state are obtained. Then, by regarding the cross-diffusion coefficient d1 as a bifurcation parameter, we will derive a bifurcation theorem for the corresponding nonlinear cross-diffusion model. Moreover, by applying spectrum theory, perturbation of simple eigenvalues and linearized stability, it is discovered that the bifurcation solutions possess local stability near the bifurcating point in proper conditions. These theoretical results mean that the cross-diffusion mechanism can create a coexistence environment for the preys and predator under some circumstances. Finally, a numerical example is proposed to verify our results.

具有猎物-猎物和双贝丁顿-德安吉利斯功能响应的非线性交叉扩散捕食者-猎物模型的时空模式和全局分岔
本文旨在研究具有猎物-税率和双贝丁顿-德安吉利函数反应的非线性交叉扩散捕食者-猎物模型的时空模式。首先,利用方便易用的 Crandall-Rabinowitz 分岔理论作为分析方法,得到了正稳态的时空模式。然后,将交叉扩散系数 d1 视为分岔参数,推导出相应非线性交叉扩散模型的分岔定理。此外,通过应用频谱理论、简单特征值的扰动和线性化稳定性,我们发现分岔解在适当条件下在分岔点附近具有局部稳定性。这些理论结果意味着交叉扩散机制可以在某些情况下为猎物和捕食者创造共存环境。最后,我们提出了一个数值实例来验证我们的结果。
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
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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