Shunsuke Kobayashi, T. Sakamoto, Yasuhide Uegata, S. Yazaki
{"title":"二维积分-微分反应-扩散系统的时间周期振荡六方解","authors":"Shunsuke Kobayashi, T. Sakamoto, Yasuhide Uegata, S. Yazaki","doi":"10.32917/hmj/1595901630","DOIUrl":null,"url":null,"abstract":"An oscillatory hexagonal solution in a two component reaction-di¤usion system with a non-local term is studied. By applying the center manifold theory, we obtain a four-dimensional dynamical system that informs us about the bifurcation structure around the trivial solution. Our results suggest that the oscillatory hexagonal solution can bifurcate from a stationary hexagonal solution via the Hopf bifurcation. This provides a reasonable explanation for the existence of the oscillatory hexagon.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A time-periodic oscillatory hexagonal solution in a 2-dimensional integro-differential reaction-diffusion system\",\"authors\":\"Shunsuke Kobayashi, T. Sakamoto, Yasuhide Uegata, S. Yazaki\",\"doi\":\"10.32917/hmj/1595901630\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An oscillatory hexagonal solution in a two component reaction-di¤usion system with a non-local term is studied. By applying the center manifold theory, we obtain a four-dimensional dynamical system that informs us about the bifurcation structure around the trivial solution. Our results suggest that the oscillatory hexagonal solution can bifurcate from a stationary hexagonal solution via the Hopf bifurcation. This provides a reasonable explanation for the existence of the oscillatory hexagon.\",\"PeriodicalId\":55054,\"journal\":{\"name\":\"Hiroshima Mathematical Journal\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2020-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Hiroshima Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.32917/hmj/1595901630\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hiroshima Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.32917/hmj/1595901630","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
A time-periodic oscillatory hexagonal solution in a 2-dimensional integro-differential reaction-diffusion system
An oscillatory hexagonal solution in a two component reaction-di¤usion system with a non-local term is studied. By applying the center manifold theory, we obtain a four-dimensional dynamical system that informs us about the bifurcation structure around the trivial solution. Our results suggest that the oscillatory hexagonal solution can bifurcate from a stationary hexagonal solution via the Hopf bifurcation. This provides a reasonable explanation for the existence of the oscillatory hexagon.
期刊介绍：
Hiroshima Mathematical Journal (HMJ) is a continuation of Journal of Science of the Hiroshima University, Series A, Vol. 1 - 24 (1930 - 1960), and Journal of Science of the Hiroshima University, Series A - I , Vol. 25 - 34 (1961 - 1970).
Starting with Volume 4 (1974), each volume of HMJ consists of three numbers annually. This journal publishes original papers in pure and applied mathematics. HMJ is an (electronically) open access journal from Volume 36, Number 1.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
