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Average amplitudes analysis for a phenomenological model under hydrodynamic interactions with periodic perturbation and multiplicative trichotomous noise

Author

Listed:
  • Lini Qiu

    (Center for Applied Mathematics of Guangxi Minzu University)

  • Guitian He

    (Center for Applied Mathematics of Guangxi Minzu University)

  • Yun Peng

    (Center for Applied Mathematics of Guangxi Minzu University)

  • Huijun Lv

    (Center for Applied Mathematics of Guangxi Minzu University)

  • Yujie Tang

    (Center for Applied Mathematics of Guangxi Minzu University)

Abstract

From a statistical mechanics perspective, to describe the dynamics of a tracer, a phenomenological model has been established by a generalized Langevin equation (GLE) which includes a Basset force, a periodic perturbation force, a Stokes force, an external force and a thermal noise. Using the generalized Shapiro-Loginov formula, the iterative expressions of the first moments of the system are obtained. The time series of the first moments have been extensively investigated. By analyzing the time series of the first moments of the system with different system parameters, the irregular responses of the curves are revealed and tend to be stable for a long time. Significantly, the dynamics of average amplitudes of the first moments, influenced by various system parameters, have also been addressed in detail. Especially, the monotonic and non-monotonic properties of the average amplitudes of the first moments versus the memory exponent $$\alpha $$ α are discussed.

Suggested Citation

  • Lini Qiu & Guitian He & Yun Peng & Huijun Lv & Yujie Tang, 2023. "Average amplitudes analysis for a phenomenological model under hydrodynamic interactions with periodic perturbation and multiplicative trichotomous noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(4), pages 1-20, April.
    • Handle: RePEc:spr:eurphb:v:96:y:2023:i:4:d:10.1140_epjb_s10051-023-00511-4
    DOI: 10.1140/epjb/s10051-023-00511-4
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    References listed on IDEAS

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    1. Vishwamittar, & Batra, Priyanka & Chopra, Ribhu, 2021. "Stochastic resonance in two coupled fractional oscillators with potential and coupling parameters subjected to quadratic asymmetric dichotomous noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    2. Gitterman, M., 2014. "Stochastic oscillator with random mass: New type of Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 11-21.
    3. Sandev, Trifce & Tomovski, Živorad & Dubbeldam, Johan L.A., 2011. "Generalized Langevin equation with a three parameter Mittag-Leffler noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3627-3636.
    4. He, Guitian & Guo, Dali & Tian, Yan & Li, Tiejun & Luo, Maokang, 2017. "Mittag-Leffler noise induced stochastic resonance in a generalized Langevin equation with random inherent frequency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 91-103.
    5. Thomas Franosch & Matthias Grimm & Maxim Belushkin & Flavio M. Mor & Giuseppe Foffi & László Forró & Sylvia Jeney, 2011. "Resonances arising from hydrodynamic memory in Brownian motion," Nature, Nature, vol. 478(7367), pages 85-88, October.
    6. Gitterman, M., 2012. "Oscillator with random trichotomous mass," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5343-5348.
    7. Fodor, Étienne & Grebenkov, Denis S. & Visco, Paolo & van Wijland, Frédéric, 2015. "Generalized Langevin equation with hydrodynamic backflow: Equilibrium properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 107-112.
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