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Most probable trajectories in the delayed tumor growth model excited by a multiplicative non-Gaussian noise

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  • Han, Ping
  • Xu, Wei
  • Zhang, Hongxia
  • Wang, Liang

Abstract

This paper investigates the transition phenomenon in the delayed tumor growth model under a multiplicative non-Gaussian colored noise based on the most probable trajectories. Firstly, the unified colored noise approximation and the small delay approximation are utilized to approximate the model in this paper. We then detect the effects of the time-delay, the correlation time and the noise intensity of non-Gaussian colored noise, and find that they can all promote the switch of most probable trajectories from the tumor state to the tumor-free state, namely, the most probable transition time decreases gradually. Conversely, these parameters suppress the transition of most probable trajectories from the tumor-free state to the tumor state, that is, the most probable transition time will increase successively. By analyzing the dynamics under these parameters, it is found that the noise intensity has the greatest influence on the transition behavior. Finally, it can be observed that the sum of the most probable transition time from the tumor-free state to the tumor state and from the tumor state to the tumor-free state is equal to the total observation time.

Suggested Citation

  • Han, Ping & Xu, Wei & Zhang, Hongxia & Wang, Liang, 2022. "Most probable trajectories in the delayed tumor growth model excited by a multiplicative non-Gaussian noise," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:chsofr:v:156:y:2022:i:c:s0960077922000121
    DOI: 10.1016/j.chaos.2022.111801
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    1. Wang, Kang Kang & Wang, Ya Jun & Li, Sheng Hong & Wu, Jian Cheng, 2016. "Stochastic stability and state shifts for a time-delayed cancer growth system subjected to correlated multiplicative and additive noises," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 1-13.
    2. 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.
    3. 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.
    4. 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.
    5. Chen, Xiaoli & Wu, Fengyan & Duan, Jinqiao & Kurths, Jürgen & Li, Xiaofan, 2019. "Most probable dynamics of a genetic regulatory network under stable Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 425-436.
    6. Tesfay, Daniel & Wei, Pingyuan & Zheng, Yayun & Duan, Jinqiao & Kurths, Jürgen, 2020. "Transitions between metastable states in a simplified model for the thermohaline circulation under random fluctuations," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    7. 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.
    8. 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.
    9. 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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