含时滞的血管化肿瘤生长模型的自由边界问题
Free Boundary Problem for a Vascularized Tumor Growth Model with Two Time Delays
DOI: 10.12677/PM.2024.142074, PDF,    国家自然科学基金支持
作者: 盖梦琳, 宋灵宇*, 朱妍红：长安大学理学院，陕西 西安
关键词: 肿瘤生长；血管化；时间延迟；稳定性；Hopf分歧；Tumor Growth； Angiogenesis； Time Delay； Stability； Hopf Bifurcation
摘要: 本文研究一个在营养物和抑制物同时作用下具有两个时滞的血管化肿瘤生长模型的自由边界问题。两个延迟分别代表细胞进行有丝分裂所需要的时间，以及因抑制物凋亡和自然凋亡而引起的细胞损失到完全被分解所需要的时间。文章主要讨论了稳态解的稳定性、Hopf分歧发生的条件，并运用Matlab进行数值模拟来验证Hopf分歧现象以及两个时滞与Hopf分歧之间的关系，最后分析了抑制物和营养物质参数对肿瘤生长的影响。
Abstract: The free boundary problem in a model of vascularized tumor growth with two time delays under the simultaneous action of nutrients and inhibitors was studied. The two time delays represent the time required for cells to undergo mitosis and the time required for cell loss due to inhibitor apoptosis and natural apoptosis to be completely disassembled, respectively. The article mainly discussed the stability of the steady-state solution, the conditions under which Hopf divergence oc-curs, and numerical simulations using Matlab to verify the Hopf Bifurcation phenomenon as well as the relationship between the two time delays and Hopf divergence, and finally analyzed the effects of the inhibitor and nutrient parameters on the tumor growth.
文章引用：盖梦琳, 宋灵宇, 朱妍红. 含时滞的血管化肿瘤生长模型的自由边界问题[J]. 理论数学, 2024, 14(2): 759-769. https://doi.org/10.12677/PM.2024.142074

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