{"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}
引用次数: 0
Abstract
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.
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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