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Transitions induced by time delays and cross-correlated sine-Wiener noises in a tumor–immune system interplay

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  • Guo, Wei
  • Du, Lu-Chun
  • Mei, Dong-Cheng

Abstract

A model of tumor–immune system interplay with time delays and cross-correlated sine-Wiener noises is investigated by numerical simulations for the stationary probability distribution (SPD) and stationary mean value 〈x〉st of tumor cell population. Results show that (i) the structure of the SPD transfers from bimodal to unimodal as the reaction time (τα) of the cell population to environmental constraints increases; (ii) conversely, as the time (τβ) of immune system to develop specific immune competence and the correlation time (τ) of noises increase, the structure of the SPD transfers from unimodal to bimodal; (iii) as the cross-correlated intensity (λ′) between noises increases, the transitions induced by τ are suppressed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1270-1280
    DOI: 10.1016/j.physa.2011.11.007
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    Citations

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    Cited by:

    1. 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.
    2. Yu, Dong & Lu, Lulu & Wang, Guowei & Yang, Lijian & Jia, Ya, 2021. "Synchronization mode transition induced by bounded noise in multiple time-delays coupled FitzHugh–Nagumo model," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    3. Cheng, Guanghui & Gui, Rong & Yao, Yuangen & Yi, Ming, 2019. "Enhancement of temporal regularity and degradation of spatial synchronization induced by cross-correlated sine-Wiener noises in regular and small-world neuronal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 361-369.
    4. Yuangen Yao & Wei Cao & Qiming Pei & Chengzhang Ma & Ming Yi, 2018. "Breakup of Spiral Wave and Order-Disorder Spatial Pattern Transition Induced by Spatially Uniform Cross-Correlated Sine-Wiener Noises in a Regular Network of Hodgkin-Huxley Neurons," Complexity, Hindawi, vol. 2018, pages 1-10, April.
    5. 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).
    6. 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.
    7. Zhu, Ping, 2021. "An equivalent analytical method to deal with cross-correlated exponential type noises in the nonlinear dynamic system," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    8. Hua, Mengjiao & Wu, Yu, 2022. "Transition and basin stability in a stochastic tumor growth model with immunization," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    9. Yuangen Yao & Haiyou Deng & Chengzhang Ma & Ming Yi & Jun Ma, 2017. "Impact of Bounded Noise and Rewiring on the Formation and Instability of Spiral Waves in a Small-World Network of Hodgkin-Huxley Neurons," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-13, January.
    10. Yuangen Yao & Lijian Yang & Canjun Wang & Quan Liu & Rong Gui & Juan Xiong & Ming Yi, 2018. "Subthreshold Periodic Signal Detection by Bounded Noise-Induced Resonance in the FitzHugh–Nagumo Neuron," Complexity, Hindawi, vol. 2018, pages 1-10, February.
    11. Dong, Xiaohui & Wang, Ming & Zhong, Guang-Yan & Yang, Fengzao & Duan, Weilong & Li, Jiang-Cheng & Xiong, Kezhao & Zeng, Chunhua, 2018. "Stochastic delayed kinetics of foraging colony system under non-Gaussian noise," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 1-13.
    12. Yu, Xingwang & Wang, Shengdan & Yang, Yanhua & Ma, Yuanlin & Liu, Tiantian & Wei, Yifan, 2025. "P-bifurcation and bistability arising from cross-correlated sine-Wiener bounded noises: A stochastic single-species model incorporating double Allee effects," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).
    13. Guo, Di & Li, Chun & Mei, Dong-Cheng, 2019. "Switch process induced by the sine-Wiener noises in the gene transcriptional regulatory system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1192-1202.

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