Scholarlink

<p>Macrophages are a major component of the tumor microenvironment and play a significant role in cancer development. Generally, macrophages are divided into two categories, tumor killer M1 and helper M2. In this paper, a new fractional-order delayed tumor-macrophage model is investigated, where the delay exists in the interconversion between M1 and M2. Firstly, we show the stability of fixed points by characteristic roots analysis. Next, treating the derivative order and/or the time delay as bifurcation parameter, respectively, we provide the existence conditions of a fractional-order Hopf bifurcation near the nonzero fixed points. Finally, the derivative order and/or time delay-induced switching of the fixed point from stable to unstable are illustrated by numerical simulations. The results suggest that a smaller derivative order and/or a smaller time delay could be used to control oscillations and thus avoid tumor recurrence.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Stability and Hopf bifurcation analysis in a fractional-order delayed tumor-macrophage model

  • 期刊论文

  • 发表日期：

    2025年1月18日

查看全文
  • Nan Liu,
  • Guoming Xu,
  • Hongli Yang

摘要

Macrophages are a major component of the tumor microenvironment and play a significant role in cancer development. Generally, macrophages are divided into two categories, tumor killer M1 and helper M2. In this paper, a new fractional-order delayed tumor-macrophage model is investigated, where the delay exists in the interconversion between M1 and M2. Firstly, we show the stability of fixed points by characteristic roots analysis. Next, treating the derivative order and/or the time delay as bifurcation parameter, respectively, we provide the existence conditions of a fractional-order Hopf bifurcation near the nonzero fixed points. Finally, the derivative order and/or time delay-induced switching of the fixed point from stable to unstable are illustrated by numerical simulations. The results suggest that a smaller derivative order and/or a smaller time delay could be used to control oscillations and thus avoid tumor recurrence.