一类PDGF诱导的肿瘤模型的动力学性质分析  

Dynamical Properties Analysis of a Class ofPDGF-Induced Tumor Models

作　　者：鄂玺琪 魏新 赵建涛 E Xiqi;WEI Xin;ZHAO Jiantao(School of Mathematical Science,Heilongjiang University,Harbin 150080,China)

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《吉林大学学报（理学版）》2024年第4期809-820,共12页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11901172);黑龙江省属高校基本科研业务费专项基金(批准号:2021-KYYWF-0017,2022-KYYWF-1043)。

摘　　要：考虑一个以血小板源性生长因子(PDGF)驱动的反应扩散神经胶质瘤数学模型.首先,对常微分系统给出其平衡点的稳定性分析,以趋化剂产生的速率m作为分支参数给出正平衡点附近Hopf分支的存在性,并通过规范型理论和中心流形定理给出判断由Hopf分支产生的周期解稳定性公式;其次,对反应扩散系统,得到当扩散介入后平衡点不会发生Turing不稳定性;最后,通过数值模拟验证理论分析结果.结果表明,趋化剂产生的速率m可区分神经胶质瘤的类型.We considered a platelet derived growth factor(PDGF)driven reaction-diffusion glioma mathematical model.Firstly,we gave the stability analysis of the equilibrium point for the ordinary differential system.We took the rate m generated by chemoattractant as the bifurcation parameter,gave the existence of the Hopf bifurcation near the positive equilibrium point,and then gave a formula to judge the stability of the periodic solution produced by the Hopf bifurcation through the gauge type theory and the central manifold theorem.Secondly,for reaction\|diffusion systems,we obtained that the equilibrium point did not occur Turing instability when diffusion was involved.Finally,the theoretical analysis results were verified through numerical simulation.The results show that the rate m generated by chemoattractant can be used to distinguish the types of glioma.

关 键 词：肿瘤模型 反应扩散 HOPF分支 稳定性 

分 类 号：O175.21[理学—数学]