IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v199y2025ip1s0960077925006253.html

Stochastic wave propagation dynamics and chaotic behavior under random perturbation for the fractional order Triki–Biswas model with white noise

Author

Listed:
  • Wang, Xin
  • Chen, Hang
  • Li, Dong
  • Fu, Shibo

Abstract

We study comprehensively the stochastic exact solutions for the fractional Triki–Biswas model with a multiplicative white noise and its chaotic behavior under random perturbation. Firstly, we obtain a detailed classification of stochastic propagation patterns, and analyze topological properties of these patterns as the parameters changing. Secondly, we show the affect of the noise on both the phase factor and the amplitude by computing the random averaging value of solutions to find a delay factor, which just proves that although the random white noise effects both amplitude and phase of waves, the averaging behavior of wave still keep the usual features of soliton and periodic motion and so forth. Finally, we show the chaotic behavior of the model under some random perturbations, which means that the model is sensitive for some random actions.

Suggested Citation

  • Wang, Xin & Chen, Hang & Li, Dong & Fu, Shibo, 2025. "Stochastic wave propagation dynamics and chaotic behavior under random perturbation for the fractional order Triki–Biswas model with white noise," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p1:s0960077925006253
    DOI: 10.1016/j.chaos.2025.116612
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925006253
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.116612?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Kai, Yue & Li, Yaxi & Huang, Liuke, 2022. "Topological properties and wave structures of Gilson–Pickering equation," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Zhang, Zhong-Jun & Wei, Cai-Min, 2009. "White noise solutions to the stochastic mKdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1794-1800.
    3. Hashemi, M.S., 2015. "Group analysis and exact solutions of the time fractional Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 141-149.
    4. Li, Zhao & Huang, Chun, 2023. "Bifurcation, phase portrait, chaotic pattern and optical soliton solutions of the conformable Fokas–Lenells model in optical fibers," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    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. Stanislav Yu. Lukashchuk, 2022. "On the Property of Linear Autonomy for Symmetries of Fractional Differential Equations and Systems," Mathematics, MDPI, vol. 10(13), pages 1-17, July.
    2. Ali, Karmina K. & Faridi, Waqas Ali & Tarla, Sibel, 2024. "Phase trajectories and Chaos theory for dynamical demonstration and explicit propagating wave formation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Biswas, Swapan & Ghosh, Uttam & Raut, Santanu, 2023. "Construction of fractional granular model and bright, dark, lump, breather types soliton solutions using Hirota bilinear method," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    4. Zhang, Bing-Wen, 2025. "The perturbed concatenated model of the Lakshmanan–Porsezian–Daniel and the Sasa–Satsuma equations having the Kerr law in the presence of spatio-temporal dispersion and multiplicative white noise," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).
    5. Hu, Xiang & Yin, Zhixiang, 2022. "A study of the pulse propagation with a generalized Kudryashov equation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    6. Wensheng Chen & Jalil Manafian & Khaled Hussein Mahmoud & Abdullah Saad Alsubaie & Abdullah Aldurayhim & Alabed Alkader, 2023. "Cutting-Edge Analytical and Numerical Approaches to the Gilson–Pickering Equation with Plenty of Soliton Solutions," Mathematics, MDPI, vol. 11(16), pages 1-35, August.
    7. Inc, Mustafa & Yusuf, Abdullahi & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Time-fractional Cahn–Allen and time-fractional Klein–Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 94-106.
    8. Zhao Li & Chen Peng, 2023. "Dynamics and Embedded Solitons of Stochastic Quadratic and Cubic Nonlinear Susceptibilities with Multiplicative White Noise in the Itô Sense," Mathematics, MDPI, vol. 11(14), pages 1-11, July.
    9. Bakhshandeh-Chamazkoti, Rohollah & Alipour, Mohsen, 2022. "Lie symmetries reduction and spectral methods on the fractional two-dimensional heat equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 97-107.
    10. Ghosh, Uttam & Roy, Subrata & Biswas, Swapan & Raut, Santanu, 2024. "A non-autonomous fractional granular model: Multi-shock, Breather, Periodic, Hybrid solutions and Soliton interactions," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    11. Nasreen, Naila & Yadav, Ankit & Malik, Sandeep & Hussain, Ejaz & Alsubaie, Abdullah Saad & Alsharif, Faisal, 2024. "Phase trajectories, chaotic behavior, and solitary wave solutions for (3+1)-dimensional integrable Kadomtsev–Petviashvili equation in fluid dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:199:y:2025:i:p1:s0960077925006253. 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.