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

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  • Wang, Jingnan
  • Shi, Hongbin
  • Xu, Li
  • Zang, Lu

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.

Suggested Citation

  • Wang, Jingnan & Shi, Hongbin & Xu, Li & Zang, Lu, 2022. "Hopf bifurcation and chaos of tumor-Lymphatic model with two time delays," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001321
    DOI: 10.1016/j.chaos.2022.111922
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    References listed on IDEAS

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    Cited by:

    1. Li, Danyang & Liu, Hua & Zhang, Haotian & Wei, Yumei, 2023. "Influence of multiple delays mechanisms on predator–prey model with Allee effect," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Hu, Limi & Qiu, Xiaoling, 2022. "Stability analysis of game models with fixed and stochastic delays," Applied Mathematics and Computation, Elsevier, vol. 435(C).

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