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The stability analysis of tumor-immune responses to chemotherapy system with gaussian white noises

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  • Duan, Wei-Long
  • Fang, Hui
  • Zeng, Chunhua

Abstract

The stability of tumor-immune responses to chemotherapy system driven by Gaussian white noises is researched because noises can have an important role in tumor treatment. In this system, there are several steady states. In order to explore the stability of these steady states, the upper Lyapunov exponents of linearized system in these steady states are computed by means of second-order algorithm for stochastic simulation Gaussian white noises. The results show that, one steady state is globally asymptotical stable if and only if the noises are weak, but another steady state is always unstable whether the noise is strong or weak. Moreover, the trajectory of system evolution initiating from anywhere is simulated by same algorithm, which proves preceding conclusions and exhibits the globally asymptotical stable steady state is a sink when noises are weak. In fact, the related conclusions give reference value for the effect of chemotherapy on tumor treatment.

Suggested Citation

  • Duan, Wei-Long & Fang, Hui & Zeng, Chunhua, 2019. "The stability analysis of tumor-immune responses to chemotherapy system with gaussian white noises," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 96-102.
    • Handle: RePEc:eee:chsofr:v:127:y:2019:i:c:p:96-102
    DOI: 10.1016/j.chaos.2019.06.030
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    References listed on IDEAS

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    Cited by:

    1. Duan, Wei-Long, 2020. "The stability analysis of tumor-immune responses to chemotherapy system driven by Gaussian colored noises," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Duan, Wei-Long & Lin, Ling, 2021. "Noise and delay enhanced stability in tumor-immune responses to chemotherapy system," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. Duan, Wei-Long & Fang, Hui, 2020. "The unified colored noise approximation of multidimensional stochastic dynamic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    4. Hao, Mengli & Jia, Wantao & Wang, Liang & Li, Fuxiao, 2022. "Most probable trajectory of a tumor model with immune response subjected to asymmetric Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

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