分支理论在肿瘤增长模型中的应用
Application of Bifurcation Theory in Tumor Growth Model
DOI: 10.12677/AAM.2020.97121, PDF,   
作者: 孙志强：北京化工大学数理学院，北京
关键词: 肿瘤增长；中心流形；局部分支；Tumor Growth Model； Center Manifolds； Local Bifurcation
摘要: 本文运用中心流形定理和局部分支理论研究了一个四维肿瘤增长模型的分支动态，理论证明了该模型Transcritial分支和Hopf分支的存在性。本文研究结果表明，若能通过治疗抑制肿瘤细胞的增长率到某个临界值以下，肿瘤细胞数目会在一段时间内较快地衰减至0，人体免疫系统能杀死肿瘤细胞，病人会获得痊愈。
Abstract: The paper does qualitative research on a four-dimensional tumor growth model by using center manifolds theory and local bifurcation theory and proves the existence of Transcritical bifurcation and Hopf bifurcation theoretically. It turns out that the patient will recover from the tumor within some time by self-immune system if the tumor growth rate could drop below the threshold with the treatment.
文章引用：孙志强. 分支理论在肿瘤增长模型中的应用[J]. 应用数学进展, 2020, 9(7): 1016-1027. https://doi.org/10.12677/AAM.2020.97121

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