{"title":"化学反应系统的稳定性、离散化和分岔分析","authors":"Qamar Din, Umer Saeed","doi":"10.46793/match.90-1.151d","DOIUrl":null,"url":null,"abstract":"Chemical reactions reveal all types of exotic behavior, that is, multistability, oscillation, chaos, or multistationarity. The mathematical framework of rate equations enables us to discuss steadystates, stability and oscillatory behavior of a chemical reaction. A planar cubic dynamical system governed by nonlinear differential equations induced by kinetic differential equations for a two-species chemical reaction is studied. It is investigated that system has unique positive steady state. Moreover, local dynamics of system is studied around its positive steady state. Existence and direction of Hopf bifurcation about positive equilibrium are carried out. In order to modify the bifurcating behavior, bifurcation control is investigated. Keeping in mind, a consistency preserving discretization for continuous chemical reaction system, a discrete counterpart is proposed, and its qualitative behavior is investigated. Numerical simulation along with bifurcation diagrams are provided to illustrate the mathematical investigations.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"73 1","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Stability, Discretization, and Bifurcation Analysis for a Chemical Reaction System\",\"authors\":\"Qamar Din, Umer Saeed\",\"doi\":\"10.46793/match.90-1.151d\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Chemical reactions reveal all types of exotic behavior, that is, multistability, oscillation, chaos, or multistationarity. The mathematical framework of rate equations enables us to discuss steadystates, stability and oscillatory behavior of a chemical reaction. A planar cubic dynamical system governed by nonlinear differential equations induced by kinetic differential equations for a two-species chemical reaction is studied. It is investigated that system has unique positive steady state. Moreover, local dynamics of system is studied around its positive steady state. Existence and direction of Hopf bifurcation about positive equilibrium are carried out. In order to modify the bifurcating behavior, bifurcation control is investigated. Keeping in mind, a consistency preserving discretization for continuous chemical reaction system, a discrete counterpart is proposed, and its qualitative behavior is investigated. Numerical simulation along with bifurcation diagrams are provided to illustrate the mathematical investigations.\",\"PeriodicalId\":51115,\"journal\":{\"name\":\"Match-Communications in Mathematical and in Computer Chemistry\",\"volume\":\"73 1\",\"pages\":\"\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Match-Communications in Mathematical and in Computer Chemistry\",\"FirstCategoryId\":\"92\",\"ListUrlMain\":\"https://doi.org/10.46793/match.90-1.151d\",\"RegionNum\":2,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Match-Communications in Mathematical and in Computer Chemistry","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.46793/match.90-1.151d","RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Stability, Discretization, and Bifurcation Analysis for a Chemical Reaction System
Chemical reactions reveal all types of exotic behavior, that is, multistability, oscillation, chaos, or multistationarity. The mathematical framework of rate equations enables us to discuss steadystates, stability and oscillatory behavior of a chemical reaction. A planar cubic dynamical system governed by nonlinear differential equations induced by kinetic differential equations for a two-species chemical reaction is studied. It is investigated that system has unique positive steady state. Moreover, local dynamics of system is studied around its positive steady state. Existence and direction of Hopf bifurcation about positive equilibrium are carried out. In order to modify the bifurcating behavior, bifurcation control is investigated. Keeping in mind, a consistency preserving discretization for continuous chemical reaction system, a discrete counterpart is proposed, and its qualitative behavior is investigated. Numerical simulation along with bifurcation diagrams are provided to illustrate the mathematical investigations.
期刊介绍：
MATCH Communications in Mathematical and in Computer Chemistry publishes papers of original research as well as reviews on chemically important mathematical results and non-routine applications of mathematical techniques to chemical problems. A paper acceptable for publication must contain non-trivial mathematics or communicate non-routine computer-based procedures AND have a clear connection to chemistry. Papers are published without any processing or publication charge.
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