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Stochastic bifurcation for a tumor–immune system with symmetric Lévy noise

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  • Xu, Yong
  • Feng, Jing
  • Li, JuanJuan
  • Zhang, Huiqing

Abstract

In this paper, we investigate stochastic bifurcation for a tumor–immune system in the presence of a symmetric non-Gaussian Lévy noise. Stationary probability density functions will be numerically obtained to define stochastic bifurcation via the criteria of its qualitative change, and bifurcation diagram at parameter plane is presented to illustrate the bifurcation analysis versus noise intensity and stability index. The effects of both noise intensity and stability index on the average tumor population are also analyzed by simulation calculation. We find that stochastic dynamics induced by Gaussian and non-Gaussian Lévy noises are quite different.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:20:p:4739-4748
    DOI: 10.1016/j.physa.2013.06.010
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    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401, December.
    2. Chiarella, Carl & He, Xue-Zhong & Wang, Duo & Zheng, Min, 2008. "The stochastic bifurcation behaviour of speculative financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3837-3846.
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    Citations

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    Cited by:

    1. 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.
    2. 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).
    3. Liu, Pei & Ning, Li Juan, 2016. "Transitions induced by cross-correlated bounded noises and time delay in a genotype selection model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 441(C), pages 32-39.
    4. Cui, Yingxue & Ning, Lijuan, 2023. "Transport of coupled particles in fractional feedback ratchet driven by Bounded noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    5. Das, Parthasakha & Das, Pritha & Mukherjee, Sayan, 2020. "Stochastic dynamics of Michaelis–Menten kinetics based tumor-immune interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    6. Cao, Boqiang & Shan, Meijing & Zhang, Qimin & Wang, Weiming, 2017. "A stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 127-143.
    7. Wang, Xiao & Duan, Jinqiao & Li, Xiaofan & Luan, Yuanchao, 2015. "Numerical methods for the mean exit time and escape probability of two-dimensional stochastic dynamical systems with non-Gaussian noises," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 282-295.
    8. 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).
    9. 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.
    10. Liu, Yuting & Shan, Meijing & Lian, Xinze & Wang, Weiming, 2016. "Stochastic extinction and persistence of a parasite–host epidemiological model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 586-602.
    11. 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).
    12. Fahimi, Milad & Nouri, Kazem & Torkzadeh, Leila, 2020. "Chaos in a stochastic cancer model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    13. Hua, Mengjiao & Wu, Yu, 2022. "Transition and basin stability in a stochastic tumor growth model with immunization," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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