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Transition and resonance induced by colored noises in tumor model under immune surveillance

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Abstract

In this paper, we study stationary probability distribution and stochastic resonance phenomenon in a tumor model under immune surveillance, which is driven by colored Gaussian noises. The signal-to-noise ratio is calculated when periodic signal is introduced. The impacts of self-correlation times \(\tau _{1}\) and \(\tau _{2}\), cross-correlation strength \(\lambda \) between two noises and time \(\tau _{3}\) on stationary probability distribution and signal-to-noise ratio are discussed, respectively. Research results show that structure of stationary probability distribution transfers from extinction state to tumor stable one as \(\lambda \), \(\tau _{1}\), \(\tau _{2}\) and \(\tau _{3}\) increase; signal-to-noise ratio as a function of additive noise intensity exhibits maximum and minimum, maximum and minimum are the identifying characteristics of stochastic resonance and stochastic reverse-resonance phenomenon. However for the curve of signal-to-noise ratio as a function of multiplicative noise intensity, there exhibits only a maximum and increases of \(\lambda \), \(\tau _{1}\) and \(\tau _{3}\) weakens the stochastic resonance and stochastic reverse-resonance; conversely, increase of \(\tau _{2}\) enhances stochastic resonance and stochastic reverse-resonance in tumor model under immune surveillance.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No. 11305079), the Natural Science Foundation of Yunnan Province (under 2010CD031) and the Key Project of Research Fund of Education Department of Yunnan Province (under 2001Z011).

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Authors and Affiliations

  1. Faculty of Science, Kunming University of Science and Technology, Kunming , 650093, Yunnan, China

    T. Yang, Q. L. Han, C. H. Zeng, Z. Q. Liu, C. Zhang & D. Tian

  2. State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming , 650093, China

    C. H. Zeng & H. Wang

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  1. T. Yang
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  2. Q. L. Han
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  3. C. H. Zeng
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  4. H. Wang
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  5. Z. Q. Liu
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Correspondence to C. H. Zeng.

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Yang, T., Han, Q.L., Zeng, C.H. et al. Transition and resonance induced by colored noises in tumor model under immune surveillance. Indian J Phys 88, 1211–1219 (2014). https://doi.org/10.1007/s12648-014-0521-7

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  • DOI: https://doi.org/10.1007/s12648-014-0521-7

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