{"title":"Pattern dynamics of a Lotka-Volterra model with taxis mechanism","authors":"","doi":"10.1016/j.amc.2024.129017","DOIUrl":null,"url":null,"abstract":"<div><p>This paper deals with the Turing bifurcation and pattern dynamics of a Lotka-Volterra model with the predator-taxis and the homogeneous no-flux boundary conditions. To investigate the pattern dynamics, we first give the occurrence conditions of the Turing bifurcation. It is found that there is no Turing bifurcation when predator-taxis disappears, while the Turing bifurcation occurs as predator-taxis is presented. Next, we establish the amplitude equation by virtue of weakly nonlinear analysis. Our theoretical result suggests the Lotka-Volterra model admits the supercritical or subcritical Turing bifurcation. In this manner, we can determine the stability of the bifurcating solution. Finally, some numerical simulation results verify the validity of the theoretical analysis. The stripe pattern, the mixed patterns, and wave patterns are performed. Interestingly, the stable stripe patterns will be broken and become wave patterns when the predator-taxis parameter is far from the Turing bifurcation critical point.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5000,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0096300324004788/pdfft?md5=f8cf98838e8b1de304adee529c2c2fc2&pid=1-s2.0-S0096300324004788-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300324004788","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper deals with the Turing bifurcation and pattern dynamics of a Lotka-Volterra model with the predator-taxis and the homogeneous no-flux boundary conditions. To investigate the pattern dynamics, we first give the occurrence conditions of the Turing bifurcation. It is found that there is no Turing bifurcation when predator-taxis disappears, while the Turing bifurcation occurs as predator-taxis is presented. Next, we establish the amplitude equation by virtue of weakly nonlinear analysis. Our theoretical result suggests the Lotka-Volterra model admits the supercritical or subcritical Turing bifurcation. In this manner, we can determine the stability of the bifurcating solution. Finally, some numerical simulation results verify the validity of the theoretical analysis. The stripe pattern, the mixed patterns, and wave patterns are performed. Interestingly, the stable stripe patterns will be broken and become wave patterns when the predator-taxis parameter is far from the Turing bifurcation critical point.
期刊介绍:
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.