{"title":"分数阶癌症系统中的混沌","authors":"I. N’Doye, H. Voos, M. Darouach","doi":"10.1109/ECC.2014.6862202","DOIUrl":null,"url":null,"abstract":"This paper deals with the fractional-order cancer system. It is based on the chaotic system concept, where the mathematical model of system contains fractional-order derivatives. We develop a fractional-order dynamical model of cancer growth, which includes the interactions between healthy tissue cells, tumor cells, and activated immune system cells, clearly leading to chaotic behavior. We perform equilibrium point analysis, indicate the conditions where chaotic dynamics can be observed, and show the existence of chaos. The behavior and stability analysis of the integer-order and the fractional commensurate and non-commensurate order cancer system with total order less than 3, which exhibits chaos, are presented as well.","PeriodicalId":251538,"journal":{"name":"2014 European Control Conference (ECC)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Chaos in a fractional-order cancer system\",\"authors\":\"I. N’Doye, H. Voos, M. Darouach\",\"doi\":\"10.1109/ECC.2014.6862202\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper deals with the fractional-order cancer system. It is based on the chaotic system concept, where the mathematical model of system contains fractional-order derivatives. We develop a fractional-order dynamical model of cancer growth, which includes the interactions between healthy tissue cells, tumor cells, and activated immune system cells, clearly leading to chaotic behavior. We perform equilibrium point analysis, indicate the conditions where chaotic dynamics can be observed, and show the existence of chaos. The behavior and stability analysis of the integer-order and the fractional commensurate and non-commensurate order cancer system with total order less than 3, which exhibits chaos, are presented as well.\",\"PeriodicalId\":251538,\"journal\":{\"name\":\"2014 European Control Conference (ECC)\",\"volume\":\"23 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2014 European Control Conference (ECC)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ECC.2014.6862202\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2014 European Control Conference (ECC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ECC.2014.6862202","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper deals with the fractional-order cancer system. It is based on the chaotic system concept, where the mathematical model of system contains fractional-order derivatives. We develop a fractional-order dynamical model of cancer growth, which includes the interactions between healthy tissue cells, tumor cells, and activated immune system cells, clearly leading to chaotic behavior. We perform equilibrium point analysis, indicate the conditions where chaotic dynamics can be observed, and show the existence of chaos. The behavior and stability analysis of the integer-order and the fractional commensurate and non-commensurate order cancer system with total order less than 3, which exhibits chaos, are presented as well.
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