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Diffusion and memory effect in a stochastic process and the correspondence to an information propagation in a social system

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  • Wang, Peng
  • Huo, Jie
  • Wang, Xu-Ming
  • Wang, Bing-Hong

Abstract

A generalized Langevin equation is suggested to describe a diffusion particle system with memory. The equation can be transformed into the Fokker–Planck equation by using the Kramers–Moyal expansion. The solution of Fokker–Planck equation can describe not only the diffusion of particles but also that of opinion particles based on the similarities between the two. We find that the memory can restrain some non-equilibrium phenomena of velocity distribution in the system, without memory, induced by correlation between the noise and space (Wang et al., 2021). However, the memory can enhance the effective collision among particles as shown by the variation of diffusion coefficients, and changes the diffusion mode between the dissipative and pumping region by comparing with that in the aforementioned system without memory. As the discussions in this physical system is paralleled to a social system, the random diffusion of social ideology, such as the information propagation, can be suppressed by the correlation between the noise and space.

Suggested Citation

  • Wang, Peng & Huo, Jie & Wang, Xu-Ming & Wang, Bing-Hong, 2022. "Diffusion and memory effect in a stochastic process and the correspondence to an information propagation in a social system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    • Handle: RePEc:eee:phsmap:v:607:y:2022:i:c:s0378437122007646
    DOI: 10.1016/j.physa.2022.128206
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    References listed on IDEAS

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    1. L. Jiang & D. Hua & J. Zhu & B. Wang & T. Zhou, 2008. "Opinion dynamics on directed small-world networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(2), pages 251-255, September.
    2. Rocco, Andrea & West, Bruce J., 1999. "Fractional calculus and the evolution of fractal phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 265(3), pages 535-546.
    3. Tajie H. Harris & Edward J. Banigan & David A. Christian & Christoph Konradt & Elia D. Tait Wojno & Kazumi Norose & Emma H. Wilson & Beena John & Wolfgang Weninger & Andrew D. Luster & Andrea J. Liu &, 2012. "Generalized Lévy walks and the role of chemokines in migration of effector CD8+ T cells," Nature, Nature, vol. 486(7404), pages 545-548, June.
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    Cited by:

    1. Wang, Peng & Zhang, Yang & Zhang, Peng-Juan & Huo, Jie & Wang, Xu-Ming & Wang, Bing-Hong, 2023. "Nonequilibrium transport characteristics of substances in a rough potential field," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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