Hopf bifurcation and chaos of tumor-Lymphatic model with two time delays

Jingnan Wang, Hongbin Shi, Li Xu and Lu Zang

Chaos, Solitons & Fractals, 2022, vol. 157, issue C

Abstract: In this paper, a tumor and Lymphatic immune system interaction model with two time delays is discussed in which the delays describe the proliferation of tumor cells and the transmission from immature T lymphocytes to mature T lymphocytes respectively. Conditions for the asymptotic stability of the equilibrium and the existence of Hopf bifurcations are obtained by analyzing the roots of a characteristic equation. The computing formulas for the stability and the direction of the Hopf bifurcating periodic solutions are given. Numerical simulation show that different values of time delays can generate different behaviors, including the stable-state, the periodic oscillation and the chaotic attractors, as well as the coexistence of two periodic oscillations. These theoretical and numerical results not only can be useful for explaining the occurrence of chaotic attractors, but also can help for understanding the biomedical significance corresponding to the interaction dynamics of tumor cells and T lymphocytes.

Keywords: Time delay; Stability; Hopf bifurcation; Tumor-immune (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001321

DOI: 10.1016/j.chaos.2022.111922

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