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The stability analysis of tumor-immune responses to chemotherapy system driven by Gaussian colored noises

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  • Duan, Wei-Long

Abstract

The influence of Gaussian colored noises on the stability of tumor-immune responses to chemotherapy system is analyzed. By means of the unified colored noise approximation of multidimensional stochastic dynamic system, the system is changed into the stochastic system with Gaussian white noises. I derive the analytic formula of the maximum Lyapunov exponent of system as a function of intensities and correlation times of Gaussian colored noises, then I find the noise-enhanced stability phenomenon, which is detected by the maximum Lyapunov exponent. Moreover, the correlation time τ1 of ξ1(t) influences the stability of steady state becomes unstable if τ1 → 0.15, which also increases as the correlation time τ2 of ξ2(t) increases. These indicate that, once tumor grows, by controlling the stochastic effect in process of chemotherapy, such as Gaussian colored noises, it is possible to control the stability of the tumor, which is very important for treatment. Especially, one could regulate the correlation time τ1 for this purpose.

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  • 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).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920306998
    DOI: 10.1016/j.chaos.2020.110303
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    Cited by:

    1. Ping, Zhu, 2023. "Analytical equivalent transformation method for nonlinear stochastic dynamics with multiple noises in high dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 176(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).

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