{"title":"俄勒冈模型的定性分析","authors":"Jun Zhou","doi":"10.4064/ap200321-18-8","DOIUrl":null,"url":null,"abstract":". In this paper, we consider the properties of the solutions for the Oregonator system, which is the mathematical model of the celebrated Belousov–Zhabotinski˘ı reaction. We first investigate the dynamics of the model, and some fundamental analytic properties such as attractive rectangle and stability of the constant solution are estab-lished. Then, we consider the steady states of the model, and the existence and nonexistence of nonconstant steady states under various conditions on the parameters and the size of the reactor.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Qualitative analysis of the Oregonator model\",\"authors\":\"Jun Zhou\",\"doi\":\"10.4064/ap200321-18-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In this paper, we consider the properties of the solutions for the Oregonator system, which is the mathematical model of the celebrated Belousov–Zhabotinski˘ı reaction. We first investigate the dynamics of the model, and some fundamental analytic properties such as attractive rectangle and stability of the constant solution are estab-lished. Then, we consider the steady states of the model, and the existence and nonexistence of nonconstant steady states under various conditions on the parameters and the size of the reactor.\",\"PeriodicalId\":55513,\"journal\":{\"name\":\"Annales Polonici Mathematici\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Polonici Mathematici\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4064/ap200321-18-8\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Polonici Mathematici","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/ap200321-18-8","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
. In this paper, we consider the properties of the solutions for the Oregonator system, which is the mathematical model of the celebrated Belousov–Zhabotinski˘ı reaction. We first investigate the dynamics of the model, and some fundamental analytic properties such as attractive rectangle and stability of the constant solution are estab-lished. Then, we consider the steady states of the model, and the existence and nonexistence of nonconstant steady states under various conditions on the parameters and the size of the reactor.
期刊介绍：
Annales Polonici Mathematici is a continuation of Annales de la Société Polonaise de Mathématique (vols. I–XXV) founded in 1921 by Stanisław Zaremba.
The journal publishes papers in Mathematical Analysis and Geometry. Each volume appears in three issues.
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