具有非局部空间记忆的反应-扩散方程中的时空动力学

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-21 DOI:10.1137/22m1543860

Shuyang Xue, Yongli Song, Hao Wang

{"title":"具有非局部空间记忆的反应-扩散方程中的时空动力学","authors":"Shuyang Xue, Yongli Song, Hao Wang","doi":"10.1137/22m1543860","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 641-667, March 2024. <br/>Abstract.To model a single-species cognitive movement, we formulate a reaction-diffusion equation with nonlocal spatial memory and investigate its dynamics. We explore the influence of the perceptual scale on the stability and Turing bifurcation. When the random diffusion is dominant, the perceptual scale does not affect the stability, but when the memory-based diffusion is dominant, there exist Turing bifurcations induced by the perceptual scale. Then the joint effect of the perceptual scale and the memory delay on the stability and spatio-temporal dynamics is investigated to show rich spatio-temporal dynamics via Turing–Hopf bifurcation and double Hopf bifurcation. Finally, we apply our analysis to an application and illustrate our theoretical results with numerical simulations.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Spatio-temporal Dynamics in a Reaction-Diffusion Equation with Nonlocal Spatial Memory\",\"authors\":\"Shuyang Xue, Yongli Song, Hao Wang\",\"doi\":\"10.1137/22m1543860\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 641-667, March 2024. <br/>Abstract.To model a single-species cognitive movement, we formulate a reaction-diffusion equation with nonlocal spatial memory and investigate its dynamics. We explore the influence of the perceptual scale on the stability and Turing bifurcation. When the random diffusion is dominant, the perceptual scale does not affect the stability, but when the memory-based diffusion is dominant, there exist Turing bifurcations induced by the perceptual scale. Then the joint effect of the perceptual scale and the memory delay on the stability and spatio-temporal dynamics is investigated to show rich spatio-temporal dynamics via Turing–Hopf bifurcation and double Hopf bifurcation. Finally, we apply our analysis to an application and illustrate our theoretical results with numerical simulations.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-02-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/22m1543860\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/22m1543860","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

SIAM 应用动力系统期刊》，第 23 卷第 1 期，第 641-667 页，2024 年 3 月。摘要：为了模拟单物种认知运动，我们提出了一个具有非局部空间记忆的反应-扩散方程，并研究了它的动力学。我们探讨了感知尺度对稳定性和图灵分岔的影响。当随机扩散占主导地位时，知觉尺度不影响稳定性，但当基于记忆的扩散占主导地位时，存在由知觉尺度诱发的图灵分岔。然后，我们研究了感知尺度和记忆延迟对稳定性和时空动态的共同影响，通过图灵-霍普夫分岔和双霍普夫分岔展示了丰富的时空动态。最后，我们将分析应用于数值模拟，以说明我们的理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Spatio-temporal Dynamics in a Reaction-Diffusion Equation with Nonlocal Spatial Memory

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 641-667, March 2024.
Abstract.To model a single-species cognitive movement, we formulate a reaction-diffusion equation with nonlocal spatial memory and investigate its dynamics. We explore the influence of the perceptual scale on the stability and Turing bifurcation. When the random diffusion is dominant, the perceptual scale does not affect the stability, but when the memory-based diffusion is dominant, there exist Turing bifurcations induced by the perceptual scale. Then the joint effect of the perceptual scale and the memory delay on the stability and spatio-temporal dynamics is investigated to show rich spatio-temporal dynamics via Turing–Hopf bifurcation and double Hopf bifurcation. Finally, we apply our analysis to an application and illustrate our theoretical results with numerical simulations.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

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.