IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v175y2023ip1s0960077923008664.html
   My bibliography  Save this article

An investigation of the survival probability for chaotic diffusion in a family of discrete Hamiltonian mappings

Author

Listed:
  • Borin, Daniel
  • Livorati, André Luís Prando
  • Leonel, Edson Denis

Abstract

Diffusive processes usually model the transport of particles in nonlinear systems. Complete chaos leads to normal diffusion, while mixed phase space gives rise to a phenomenon called stickiness, leading to anomalous diffusion. We investigate the survival probability that a particle moving along a chaotic region in a mixed-phase space has to survive a specific domain. We show along the chaotic part far from islands that an exponential decay describes the survival probability. Nonetheless, when the islands are incorporated into the domain, the survival probability exhibits an exponential decay for a short time, changing to a slower decay for a considerable enough time. This changeover is a signature of stickiness. We solve the diffusion equation by obtaining the probability density to observe a given particle along a specific region within a certain time interval. Integrating the probability density for a defined phase space area provides analytical survival probability. Numerical simulations fit well the analytical findings for the survival probability when the region is fully chaotic. However, the agreement could be better when mixed structure with islands and periodic areas are included in the domain.

Suggested Citation

  • Borin, Daniel & Livorati, André Luís Prando & Leonel, Edson Denis, 2023. "An investigation of the survival probability for chaotic diffusion in a family of discrete Hamiltonian mappings," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008664
    DOI: 10.1016/j.chaos.2023.113965
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923008664
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113965?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. Oliveira, Tulio M. & Artuso, Roberto & Manchein, Cesar, 2019. "Collapse of hierarchical phase space and mixing rates in Hamiltonian systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 530(C).
    2. Hilfer, R., 2003. "On fractional diffusion and continuous time random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 35-40.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Borin, Daniel, 2024. "Caputo fractional standard map: Scaling invariance analyses," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Oğul Esen & Cristina Sardón & Marcin Zajac, 2024. "A Discrete Hamilton–Jacobi Theory for Contact Hamiltonian Dynamics," Mathematics, MDPI, vol. 12(15), pages 1-24, July.

    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. Zhao, Yongqiang & Tang, Yanbin, 2024. "Critical behavior of a semilinear time fractional diffusion equation with forcing term depending on time and space," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Gorenflo, Rudolf & Mainardi, Francesco & Vivoli, Alessandro, 2007. "Continuous-time random walk and parametric subordination in fractional diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 34(1), pages 87-103.
    3. Allahviranloo, T. & Gouyandeh, Z. & Armand, A., 2015. "Numerical solutions for fractional differential equations by Tau-Collocation method," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 979-990.
    4. Gafiychuk, V.V. & Datsko, B.Yo., 2006. "Pattern formation in a fractional reaction–diffusion system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 300-306.
    5. Jaros{l}aw Klamut & Tomasz Gubiec, 2018. "Directed Continuous-Time Random Walk with memory," Papers 1807.01934, 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:chsofr:v:175:y:2023:i:p1:s0960077923008664. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.