带有外部治疗的癌症模型的动力学分析

Dynamic Analysis of Cancer Model withExternal Therapy

摘要: 众所周知，癌症一直是威胁人类生命健康的重大疾病之一，关于它的内在发病机理是很多科学家重点关注的研究课题。本文中我们将充分利用动力系统分支理论知识和数值模拟来研究与癌症相关的各类动力学行动，力求完整地揭示与癌症相关的分支现象背后的医学意义，并对病情未来发展趋势的预存提供积极的帮助。在本文中我们主要研究了刻画肿瘤细胞和免疫效应细胞的二维癌症模型的动力学行为，得到了平衡点的个数和类型，证明了余维2的Hopf分支和余维2的Bogdanov-Takens分支的存在性。最后通过数值模拟验证了所得结论。

Abstract: As we all know, cancer has always been one of the major diseases threatening lifeand health, and its intrinsic pathogenesis is an important research topic that manyscents OCUS On this paper, we will make full use of bifurcation theory ofdynamical systems and numerical simulations to study various dynamics related tocancer, striving to fully reveal the medical significance of bifurcation related to cancer.and provide positive help for predicting the future development trend of the diseaseWe mainly study the dynamics of a two-dimensional cancer model involving tumocells and immune effector cells. We obtain the number and type of equilibrium points.verify the Hopf bifurcation of codimension 2 and the Bogdanov-takens bifurcation ofcodimension 2. Finally the conclusions obtained are verified by numerical simulation.