IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v554y2020ics0378437120303101.html
   My bibliography  Save this article

Localization phase transition in stochastic dynamics on networks with hub topology

Author

Listed:
  • Seroussi, Inbar
  • Sochen, Nir

Abstract

Dynamics among central sources (hubs) providing a resource and large number of components enjoying and contributing to this resource describes many real life situations. Modeling, controlling, and balancing this dynamics is a challenging problem that arises in many scientific disciplines. We analyze a stochastic dynamical system exhibiting this dynamics with a multiplicative noise. We show that this model can be solved exactly by passing to variables that describe the mass ratio between the components and the hub. We derive a deterministic equation for the average mass ratio in the absence of noise on the hub. This equation describes logistic growth. We derive the phase diagram of the model with and without noise on the hub. We show that when there in no noise on the hub there is no localization phase. In the presence of noise on the hub, we identify two regimes by deriving the equilibrium distribution of the process. The first regime describes balance between the non-hub components and the hub, in the second regime the resource is concentrated mainly on the hub. We generalize the results to a system with multiple hubs. We show that there is less concentration on the hubs as the number of hubs increases, and in the limit of infinite hubs the average mass ratio grows or decays exponentially. Surprisingly, in the limit of large number of components the transition values do not depend on the amount of resource given by the non-hub nodes. We propose an interesting application of this model in the context of porous media using Magnetic Resonance (MR) techniques.

Suggested Citation

  • Seroussi, Inbar & Sochen, Nir, 2020. "Localization phase transition in stochastic dynamics on networks with hub topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
  • Handle: RePEc:eee:phsmap:v:554:y:2020:i:c:s0378437120303101
    DOI: 10.1016/j.physa.2020.124636
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437120303101
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2020.124636?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 2000. "Scale-free characteristics of random networks: the topology of the world-wide web," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 69-77.
    2. Jean-Philippe Bouchaud & Marc Mezard, 2000. "Wealth condensation in a simple model of economy," Science & Finance (CFM) working paper archive 500026, Science & Finance, Capital Fund Management.
    3. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    4. Jean-Philippe Bouchaud, 2015. "On growth-optimal tax rates and the issue of wealth inequalities," Papers 1508.00275, arXiv.org, revised Aug 2015.
    5. Takashi Ichinomiya, 2012. "Bouchaud-M\'ezard model on a random network," Papers 1209.2467, arXiv.org.
    6. Bouchaud, Jean-Philippe & Mézard, Marc, 2000. "Wealth condensation in a simple model of economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(3), pages 536-545.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stojkoski, Viktor & Karbevski, Marko & Utkovski, Zoran & Basnarkov, Lasko & Kocarev, Ljupco, 2021. "Evolution of cooperation in networked heterogeneous fluctuating environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    2. Zhiyuan Liu & R. A. Serota, 2017. "On absence of steady state in the Bouchaud-M\'ezard network model," Papers 1704.02377, arXiv.org.
    3. Chong, Carsten & Klüppelberg, Claudia, 2019. "Partial mean field limits in heterogeneous networks," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 4998-5036.
    4. Ole Peters & Alexander Adamou, 2018. "The sum of log-normal variates in geometric Brownian motion," Papers 1802.02939, arXiv.org.
    5. Kemp, Jordan T. & Bettencourt, Luís M.A., 2022. "Statistical dynamics of wealth inequality in stochastic models of growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    6. M. Dashti Moghaddam & Zhiyuan Liu & R. A. Serota, 2019. "Distributions of Historic Market Data -- Relaxation and Correlations," Papers 1907.05348, arXiv.org, revised Feb 2020.
    7. Liu, Z. & Serota, R.A., 2017. "Correlation and relaxation times for a stochastic process with a fat-tailed steady-state distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 301-311.
    8. Venkatasubramanian, Venkat & Luo, Yu & Sethuraman, Jay, 2015. "How much inequality in income is fair? A microeconomic game theoretic perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 120-138.
    9. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    10. Tamotsu Onozaki, 2018. "Nonlinearity, Bounded Rationality, and Heterogeneity," Springer Books, Springer, number 978-4-431-54971-0, January.
    11. Smerlak, Matteo, 2016. "Thermodynamics of inequalities: From precariousness to economic stratification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 441(C), pages 40-50.
    12. Marco Raberto & Silvano Cincotti & Sergio Focardi & Michele Marchesi, 2003. "Traders' Long-Run Wealth in an Artificial Financial Market," Computational Economics, Springer;Society for Computational Economics, vol. 22(2), pages 255-272, October.
    13. Jiong Liu & R. A. Serota, 2023. "Rethinking Generalized Beta family of distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(2), pages 1-14, February.
    14. Geoff Willis & Juergen Mimkes, 2004. "Evidence for the Independence of Waged and Unwaged Income, Evidence for Boltzmann Distributions in Waged Income, and the Outlines of a Coherent Theory of Income Distribution," Microeconomics 0408001, University Library of Munich, Germany.
    15. G. Willis, 2004. "Laser Welfare: First Steps in Econodynamic Engineering," Papers cond-mat/0408227, arXiv.org.
    16. Alessandro Pluchino & Alessio Emanuele Biondo & Andrea Rapisarda, 2018. "Talent Versus Luck: The Role Of Randomness In Success And Failure," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 21(03n04), pages 1-31, May.
    17. Michele Vodret & Iacopo Mastromatteo & Bence Tóth & Michael Benzaquen, 2023. "Microfounding GARCH models and beyond: a Kyle-inspired model with adaptive agents," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 18(3), pages 599-625, July.
    18. Ma, Tao & Holden, John G. & Serota, R.A., 2013. "Distribution of wealth in a network model of the economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2434-2441.
    19. Zoltan Kuscsik & Denis Horvath, 2007. "Statistical properties of agent-based market area model," Papers 0710.0459, arXiv.org.
    20. Istvan Gere & Szabolcs Kelemen & Geza Toth & Tamas Biro & Zoltan Neda, 2021. "Wealth distribution in modern societies: collected data and a master equation approach," Papers 2104.04134, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:554:y:2020:i:c:s0378437120303101. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.