{"title":"Integrability Analysis of the Smallest 3D Biochemical Reaction Model","authors":"A. Amen","doi":"10.46793/match.90-2.333a","DOIUrl":null,"url":null,"abstract":"In this paper the complex dynamics of a smallest biochemical system model in three-dimensional systems with the reaction scheme. This model is described by a system of three nonlinear ordinary differential equations with five positive real parameters, are analyzed and studied. We present a thorough analysis of their invariant algebraic surfaces and exponential factors and investigate the integrability and nonintegrabilty of this model. Particularly, we show the non-existence of polynomial, rational, Darboux and local analytic first integrals in a neighborhood of the equilibrium. Moreover, we prove that, the model is not integrable in the sense of Bogoyavlensky in the class of rational functions.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2023-04-01","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.90-2.333a","RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper the complex dynamics of a smallest biochemical system model in three-dimensional systems with the reaction scheme. This model is described by a system of three nonlinear ordinary differential equations with five positive real parameters, are analyzed and studied. We present a thorough analysis of their invariant algebraic surfaces and exponential factors and investigate the integrability and nonintegrabilty of this model. Particularly, we show the non-existence of polynomial, rational, Darboux and local analytic first integrals in a neighborhood of the equilibrium. Moreover, we prove that, the model is not integrable in the sense of Bogoyavlensky in the class of rational functions.
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.