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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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    1. Spagnolo, B. & Valenti, D. & Guarcello, C. & Carollo, A. & Persano Adorno, D. & Spezia, S. & Pizzolato, N. & Di Paola, B., 2015. "Noise-induced effects in nonlinear relaxation of condensed matter systems," Chaos, Solitons & Fractals, Elsevier, vol. 81(PB), pages 412-424.
    2. Xu, Yong & Feng, Jing & Li, JuanJuan & Zhang, Huiqing, 2013. "Stochastic bifurcation for a tumor–immune system with symmetric Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4739-4748.
    3. Wu, Jian-Li & Duan, Wei-Long & Luo, Yuhui & Yang, Fengzao, 2020. "Time delay and non-Gaussian noise-enhanced stability of foraging colony system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    4. Liu, Xiangdong & Li, Qingze & Pan, Jianxin, 2018. "A deterministic and stochastic model for the system dynamics of tumor–immune responses to chemotherapy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 162-176.
    5. Yablokov, A.A. & Mylnikov, V.M. & Pankratov, A.L. & Pankratova, E.V. & Gordeeva, A.V., 2020. "Suppression of switching errors in weakly damped Josephson junctions," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    6. 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).
    7. Yang, Yun-Feng & Wang, Can-Jun & Yang, Ke-Li & Yang, Ya-Qiang & Zheng, Ying-Chun, 2019. "Impacts of the cross-correlated noises on the fluctuation behaviors of a gene transcriptional regulatory system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 580-591.
    8. 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.
    9. E. V. Pankratova & V. N. Belykh & E. Mosekilde, 2006. "Role of the driving frequency in a randomly perturbed Hodgkin-Huxley neuron with suprathreshold forcing," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 53(4), pages 529-536, October.
    10. Pang, Liuyong & Zhao, Zhong & Song, Xinyu, 2016. "Cost-effectiveness analysis of optimal strategy for tumor treatment," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 293-301.
    11. Uzuntarla, Muhammet & Uzun, Rukiye & Yilmaz, Ergin & Ozer, Mahmut & Perc, Matjaž, 2013. "Noise-delayed decay in the response of a scale-free neuronal network," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 202-208.
    12. A. Dubkov & B. Spagnolo, 2008. "Verhulst model with Lévy white noise excitation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(3), pages 361-367, October.
    13. Bai, Chunyan, 2018. "Time delay effects of stochastic resonance induced by multiplicative periodic signal in the gene transcriptional regulatory model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 304-311.
    14. Duan, Wei-Long & Zeng, Chunhua, 2017. "Signal power amplification of intracellular calcium dynamics with non-Gaussian noises and time delay," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 400-405.
    15. Lin, Qiao-Feng & Wang, Can-Jun & Yang, Ke-Li & Tian, Meng-Yu & Wang, Ya & Dai, Jia-Liang, 2019. "Cross-correlated bounded noises induced the population extinction and enhancement of stability in a population growth model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1046-1057.
    16. A. Fiasconaro & A. Ochab-Marcinek & B. Spagnolo & E. Gudowska-Nowak, 2008. "Monitoring noise-resonant effects in cancer growth influenced by external fluctuations and periodic treatment," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(3), pages 435-442, October.
    17. Duan, Wei-Long & Zeng, Chunhua, 2017. "Statistics for anti-synchronization of intracellular calcium dynamics," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 611-616.
    18. Tian, Meng-Yu & Wang, Can-Jun & Yang, Ke-Li & Fu, Peng & Xia, Chun-Yan & Zhuo, Xiao-Jing & Wang, Lei, 2020. "Estimating the nonlinear effects of an ecological system driven by Ornstein-Uhlenbeck noise," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    19. Bedartha Goswami & Niklas Boers & Aljoscha Rheinwalt & Norbert Marwan & Jobst Heitzig & Sebastian F. M. Breitenbach & Jürgen Kurths, 2018. "Abrupt transitions in time series with uncertainties," Nature Communications, Nature, vol. 9(1), pages 1-10, December.
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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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