{"title":"双分量反应扩散系统中霍普夫-图灵-图灵奇点的不稳定性框架","authors":"Hirofumi Izuhara, Shunusuke Kobayashi","doi":"10.1007/s13160-024-00668-0","DOIUrl":null,"url":null,"abstract":"<p>This paper investigates pattern formation in 2-component reaction–diffusion systems with linear diffusion and local reaction terms. We propose a novel instability framework characterized by 0-mode Hopf instability, <span>\\(\\textit{m}\\)</span> and <span>\\(\\textit{m}\\)</span> + 1 mode Turing instabilities in 2-component reaction–diffusion systems. A normal form for the codimension 3 bifurcation is derived via the center manifold reduction, representing one of the main results in this paper. Additionally, we present numerical results on the bifurcation of certain reaction–diffusion systems and on the chaotic behavior of the normal form.</p>","PeriodicalId":50264,"journal":{"name":"Japan Journal of Industrial and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An instability framework of Hopf–Turing–Turing singularity in 2-component reaction–diffusion systems\",\"authors\":\"Hirofumi Izuhara, Shunusuke Kobayashi\",\"doi\":\"10.1007/s13160-024-00668-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper investigates pattern formation in 2-component reaction–diffusion systems with linear diffusion and local reaction terms. We propose a novel instability framework characterized by 0-mode Hopf instability, <span>\\\\(\\\\textit{m}\\\\)</span> and <span>\\\\(\\\\textit{m}\\\\)</span> + 1 mode Turing instabilities in 2-component reaction–diffusion systems. A normal form for the codimension 3 bifurcation is derived via the center manifold reduction, representing one of the main results in this paper. Additionally, we present numerical results on the bifurcation of certain reaction–diffusion systems and on the chaotic behavior of the normal form.</p>\",\"PeriodicalId\":50264,\"journal\":{\"name\":\"Japan Journal of Industrial and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-09-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Japan Journal of Industrial and Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s13160-024-00668-0\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Japan Journal of Industrial and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13160-024-00668-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
An instability framework of Hopf–Turing–Turing singularity in 2-component reaction–diffusion systems
This paper investigates pattern formation in 2-component reaction–diffusion systems with linear diffusion and local reaction terms. We propose a novel instability framework characterized by 0-mode Hopf instability, \(\textit{m}\) and \(\textit{m}\) + 1 mode Turing instabilities in 2-component reaction–diffusion systems. A normal form for the codimension 3 bifurcation is derived via the center manifold reduction, representing one of the main results in this paper. Additionally, we present numerical results on the bifurcation of certain reaction–diffusion systems and on the chaotic behavior of the normal form.
期刊介绍:
Japan Journal of Industrial and Applied Mathematics (JJIAM) is intended to provide an international forum for the expression of new ideas, as well as a site for the presentation of original research in various fields of the mathematical sciences. Consequently the most welcome types of articles are those which provide new insights into and methods for mathematical structures of various phenomena in the natural, social and industrial sciences, those which link real-world phenomena and mathematics through modeling and analysis, and those which impact the development of the mathematical sciences. The scope of the journal covers applied mathematical analysis, computational techniques and industrial mathematics.