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Hopf bifurcation of a free boundary problem modeling tumor growth with angiogenesis and two time delays

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  • Zhou, Haihua
  • Wang, Zejia
  • Yuan, Daming
  • Song, Huijuan

Abstract

This paper concerns a free boundary problem modeling tumor growth with angiogenesis and two time delays. The two delays represent the time taken for cells to undergo mitosis and modify the rate of cell loss because of apoptosis, respectively. We study the stability of stationary solutions and find that Hopf bifurcation occurs under some conditions, which extends the results of Xu. Furthermore, numerical simulations are performed to investigate the relationship among the rate of angiogenesis, two time delays and Hopf bifurcation.

Suggested Citation

  • Zhou, Haihua & Wang, Zejia & Yuan, Daming & Song, Huijuan, 2021. "Hopf bifurcation of a free boundary problem modeling tumor growth with angiogenesis and two time delays," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p1:s0960077921009322
    DOI: 10.1016/j.chaos.2021.111578
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    References listed on IDEAS

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    1. Shihe Xu & Fangwei Zhang, 2020. "Analysis of a Delayed Free Boundary Problem with Application to a Model for Tumor Growth of Angiogenesis," Complexity, Hindawi, vol. 2020, pages 1-12, February.
    2. Xu, Shihe, 2009. "Hopf bifurcation of a free boundary problem modeling tumor growth with two time delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2491-2494.
    3. Bao Shi & Fangwei Zhang & Shihe Xu, 2011. "Hopf Bifurcation of a Mathematical Model for Growth of Tumors with an Action of Inhibitor and Two Time Delays," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-10, March.
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    Cited by:

    1. 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).
    2. Zhou, Haihua & Song, Huijuan & Wang, Zejia, 2022. "The effect of time delay in regulatory apoptosis on a tumor model with angiogenesis," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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    1. Zhou, Haihua & Song, Huijuan & Wang, Zejia, 2022. "The effect of time delay in regulatory apoptosis on a tumor model with angiogenesis," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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