Hopf-like Bifurcation Analysis of a Fractional-Order Tumor-Lymphatic Model Involving Two Time Delays

Xueying Shi; Xiaoping Chen; Chengdai Huang; An Luo; Xin Yin

doi:10.3390/sym16060775

,

and

¹

Department of Mathematics, Taizhou University, Taizhou 225300, China

²

Department of Mathematics, Southeast University, Nanjing 210096, China

³

School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China

^*

Author to whom correspondence should be addressed.

Symmetry2024, 16(6), 775;https://doi.org/10.3390/sym16060775

This article belongs to the Section Mathematics

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Abstract

This paper investigates the Hopf-like bifurcation of a fractional tumor-lymphatic model with two time delays. The two time delays are considered as branching parameters, and we analyze their influences on the dynamic properties of the model. Through an examination of the root distribution of the characteristic equation, we derive the properties of the positive steady state and the conditions for the occurrence of Hopf-like bifurcation near the positive equilibrium point. Numerical simulations are demonstrated to support our theoretical results.

Keywords:

fractional order; tumor-lymphatic model; stability; Hopf-like bifurcation; two time delays

Hopf-like Bifurcation Analysis of a Fractional-Order Tumor-Lymphatic Model Involving Two Time Delays

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