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The properties of the anti-tumor model with coupling non-Gaussian noise and Gaussian colored noise

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  • Guo, Qin
  • Sun, Zhongkui
  • Xu, Wei

Abstract

The anti-tumor model with correlation between multiplicative non-Gaussian noise and additive Gaussian-colored noise has been investigated in this paper. The behaviors of the stationary probability distribution demonstrate that the multiplicative non-Gaussian noise plays a dual role in the development of tumor and an appropriate additive Gaussian colored noise can lead to a minimum of the mean value of tumor cell population. The mean first passage time is calculated to quantify the effects of noises on the transition time of tumors between the stable states. An increase in both the non-Gaussian noise intensity and the departure from the Gaussian noise can accelerate the transition from the disease state to the healthy state. On the contrary, an increase in cross-correlated degree will slow down the transition. Moreover, the correlation time can enhance the stability of the disease state.

Suggested Citation

  • Guo, Qin & Sun, Zhongkui & Xu, Wei, 2016. "The properties of the anti-tumor model with coupling non-Gaussian noise and Gaussian colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 43-52.
    • Handle: RePEc:eee:phsmap:v:449:y:2016:i:c:p:43-52
    DOI: 10.1016/j.physa.2015.12.102
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    References listed on IDEAS

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    1. 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.
    2. Fuentes, M.A. & Wio, Horacio S. & Toral, Raúl, 2002. "Effective Markovian approximation for non-Gaussian noises: a path integral approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 303(1), pages 91-104.
    3. D. Mei & C. Xie & L. Zhang, 2004. "The stationary properties and the state transition of the tumor cell growth mode," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 41(1), pages 107-112, September.
    4. Guo, Wei & Du, Lu-Chun & Mei, Dong-Cheng, 2012. "Transitions induced by time delays and cross-correlated sine-Wiener noises in a tumor–immune system interplay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1270-1280.
    5. Zhang, Huiqing & Xu, Wei & Xu, Yong, 2009. "The study on a stochastic system with non-Gaussian noise and Gaussian colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 781-788.
    6. Guo, Wei & Mei, Dong-Cheng, 2014. "Stochastic resonance in a tumor–immune system subject to bounded noises and time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 90-98.
    7. Yang, Lin-Jing & Lv, Feng & Mei, Dong-Cheng, 2015. "Effects of periodic force on the stability of the metastable state in logistic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 331-336.
    8. Fuentes, M.A. & Toral, Raúl & Wio, Horacio S., 2001. "Enhancement of stochastic resonance: the role of non Gaussian noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 114-122.
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