IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v592y2022ics0378437121009936.html
   My bibliography  Save this article

Efficient approach to time-dependent super-diffusive Lévy random walks on finite 2D-tori using circulant analogues

Author

Listed:
  • Serrano, Alfredo Blanco
  • Allen-Perkins, Alfonso
  • Andrade, Roberto Fernandes Silva

Abstract

This work resumes the investigation on discrete-time super-diffusive in Lévy random walks defined on networks by using a inverse problem approach, with a focus on 2D-tori. Imposing that the mean square displacement of the walker should be proportional to tγ, we use a Markov Chain formalism to evaluate a fine tuned time-dependent probability distribution of long-distance jumps the walker should use to meet this dependency. Despite its wide applicability, calculations are time-intensive, with a computing time proportional to the number of nodes in the graph to a power >3.4. Here it is shown that, by using the circulant property satisfied by the adjacency matrices of a class of tori, it is possible to significantly speed up the calculations. For the purpose of comparison, the inverse super-diffusion problem is solved for two tori based on finite patches of the two-dimensional square lattice, namely the usual (non-circulant) and the helical (circulant) ones. The results of the latter, based on derived new expressions to compute the mean square displacement valid for circulant tori, are in complete agreement with those derived using general expressions, even if the computing time increases with respect to the number of nodes with a significantly smaller exponent ≳2.1. Numerical simulations in both tori types also reproduce super-diffusion when using the time-dependent probability distributions obtained for the helical one. The results suggest that this time efficient approach can be extended to model super-diffusion on cubic and hyper-cubic lattices.

Suggested Citation

  • Serrano, Alfredo Blanco & Allen-Perkins, Alfonso & Andrade, Roberto Fernandes Silva, 2022. "Efficient approach to time-dependent super-diffusive Lévy random walks on finite 2D-tori using circulant analogues," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).
    • Handle: RePEc:eee:phsmap:v:592:y:2022:i:c:s0378437121009936
    DOI: 10.1016/j.physa.2021.126833
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437121009936
    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.2021.126833?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. dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.
    2. Nicolas E. Humphries & Nuno Queiroz & Jennifer R. M. Dyer & Nicolas G. Pade & Michael K. Musyl & Kurt M. Schaefer & Daniel W. Fuller & Juerg M. Brunnschweiler & Thomas K. Doyle & Jonathan D. R. Hought, 2010. "Environmental context explains Lévy and Brownian movement patterns of marine predators," Nature, Nature, vol. 465(7301), pages 1066-1069, June.
    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. Bi, Zhimin & Liu, Shutang & Ouyang, Miao, 2022. "Spatial dynamics of a fractional predator-prey system with time delay and Allee effect," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Toman, Kellan & Voulgarakis, Nikolaos K., 2022. "Stochastic pursuit-evasion curves for foraging dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    3. dos Santos, M.A.F. & Colombo, E.H. & Anteneodo, C., 2021. "Random diffusivity scenarios behind anomalous non-Gaussian diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Hao, Mengli & Jia, Wantao & Wang, Liang & Li, Fuxiao, 2022. "Most probable trajectory of a tumor model with immune response subjected to asymmetric Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    5. Nauta, Johannes & Simoens, Pieter & Khaluf, Yara, 2022. "Group size and resource fractality drive multimodal search strategies: A quantitative analysis on group foraging," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    6. Shi, Hong-Da & Du, Lu-Chun & Huang, Fei-Jie & Guo, Wei, 2022. "Collective topological active particles: Non-ergodic superdiffusion and ageing in complex environments," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    7. Maike A. F. dos Santos, 2019. "Mittag–Leffler Memory Kernel in Lévy Flights," Mathematics, MDPI, vol. 7(9), pages 1-13, August.
    8. Wei, Q. & Yang, S. & Zhou, H.W. & Zhang, S.Q. & Li, X.N. & Hou, W., 2021. "Fractional diffusion models for radionuclide anomalous transport in geological repository systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    9. Bi, Zhimin & Liu, Shutang & Ouyang, Miao, 2022. "Three-dimensional pattern dynamics of a fractional predator-prey model with cross-diffusion and herd behavior," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    10. Wei, Wenqi & Ouyang, Haibin & Li, Steven & Zhao, Xuanbo & Zou, Dexuan, 2022. "A modified fireworks algorithm with dynamic search interval based on closed-loop control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 329-360.
    11. Alireza Khalili Golmankhaneh & Renat Timergalievich Sibatov, 2021. "Fractal Stochastic Processes on Thin Cantor-Like Sets," Mathematics, MDPI, vol. 9(6), pages 1-13, March.
    12. Muhammad Irfan & Abdul Wadood & Tahir Khurshaid & Bakht Muhammad Khan & Ki-Chai Kim & Seung-Ryle Oh & Sang-Bong Rhee, 2021. "An Optimized Adaptive Protection Scheme for Numerical and Directional Overcurrent Relay Coordination Using Harris Hawk Optimization," Energies, MDPI, vol. 14(18), pages 1-21, September.
    13. Shinohara, Shuji & Okamoto, Hiroshi & Manome, Nobuhito & Gunji, Pegio-Yukio & Nakajima, Yoshihiro & Moriyama, Toru & Chung, Ung-il, 2022. "Simulation of foraging behavior using a decision-making agent with Bayesian and inverse Bayesian inference: Temporal correlations and power laws in displacement patterns," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    14. Aranda, Orestes Tumbarell & Penna, André L.A. & Oliveira, Fernando A., 2021. "Nonlocal pattern formation effects in evolutionary population dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).

    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:592:y:2022:i:c:s0378437121009936. 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.