{"title":"肿瘤-正常细胞相互作用脉冲竞争系统的周期解","authors":"Jiawei Dou, Weiming Zheng","doi":"10.1109/ICBBE.2010.5516323","DOIUrl":null,"url":null,"abstract":"In this work we investigate a problem of existence of positive periodic solutions for a class of impulsive differential equations in the plane. This describes generally the competition between normal and tumor cells in a periodically changing environment under chemotherapeutic treatment. The mathematical problem involves a coupled system of Lotka-Volterra together with periodically pulsed conditions. We use the monotone method to construct the upper and lower sequences converging to the periodic solution of the system.","PeriodicalId":6396,"journal":{"name":"2010 4th International Conference on Bioinformatics and Biomedical Engineering","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2010-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The Periodic Solutions of Impulsive Competition System on Tumor-Normal Cell Interaction\",\"authors\":\"Jiawei Dou, Weiming Zheng\",\"doi\":\"10.1109/ICBBE.2010.5516323\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work we investigate a problem of existence of positive periodic solutions for a class of impulsive differential equations in the plane. This describes generally the competition between normal and tumor cells in a periodically changing environment under chemotherapeutic treatment. The mathematical problem involves a coupled system of Lotka-Volterra together with periodically pulsed conditions. We use the monotone method to construct the upper and lower sequences converging to the periodic solution of the system.\",\"PeriodicalId\":6396,\"journal\":{\"name\":\"2010 4th International Conference on Bioinformatics and Biomedical Engineering\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-07-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 4th International Conference on Bioinformatics and Biomedical Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICBBE.2010.5516323\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 4th International Conference on Bioinformatics and Biomedical Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICBBE.2010.5516323","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Periodic Solutions of Impulsive Competition System on Tumor-Normal Cell Interaction
In this work we investigate a problem of existence of positive periodic solutions for a class of impulsive differential equations in the plane. This describes generally the competition between normal and tumor cells in a periodically changing environment under chemotherapeutic treatment. The mathematical problem involves a coupled system of Lotka-Volterra together with periodically pulsed conditions. We use the monotone method to construct the upper and lower sequences converging to the periodic solution of the system.