IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v136y2020ics0960077920301922.html
   My bibliography  Save this article

Influence of numerical noises on computer-generated simulation of spatio-temporal chaos

Author

Listed:
  • Qin, Shijie
  • Liao, Shijun

Abstract

Due to the famous butterfly-effect, it is rather difficult to gain a reliable simulation of chaos in an interval of time that is long enough from statistic viewpoint. In this paper we propose an efficient numerical strategy of the clean numerical simulation (CNS) in physical space to gain reliable simulation of spatio-temporal chaos in a long enough interval of time by means of reducing both of truncation and round-off error to a required tiny level. Without loss of generality, the damped driven sine-Gordon equation is used to illustrate its validity for spatio-temporal chaos. The reliable result in a long interval of time given by this CNS algorithm is used as benchmark solution to investigate the influence of numerical noise (i.e. truncation and round-off error) by comparing it in details with those given by the Runge-Kutta’s method in double precision. It is found that numerical noise can lead to, both quantitatively and qualitatively, huge deviation of the spatio-temporal chaotic system not only in trajectories but also even in statistics! Therefore, in practice we should check very carefully the reliability of computer-generated simulations of spatio-temporal chaotic systems (including turbulent flows), especially when the duration of simulation is quite long. The new strategy of the CNS in physical space provides us an efficient way to accurately study lots of spatio-temporal chaotic systems in science and engineering in a long enough interval of time so as to reveal some new physical truths by means of clearing away numerical noises.

Suggested Citation

  • Qin, Shijie & Liao, Shijun, 2020. "Influence of numerical noises on computer-generated simulation of spatio-temporal chaos," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    • Handle: RePEc:eee:chsofr:v:136:y:2020:i:c:s0960077920301922
    DOI: 10.1016/j.chaos.2020.109790
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920301922
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.109790?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. Liao, Shijun, 2013. "On the numerical simulation of propagation of micro-level inherent uncertainty for chaotic dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 1-12.
    2. Altan, Aytaç & Karasu, Seçkin & Bekiros, Stelios, 2019. "Digital currency forecasting with chaotic meta-heuristic bio-inspired signal processing techniques," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 325-336.
    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. Yang, Yu & Qin, Shijie & Liao, Shijun, 2023. "Ultra-chaos of a mobile robot: A higher disorder than normal-chaos," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

    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. Cui, Li & Lu, Ming & Ou, Qingli & Duan, Hao & Luo, Wenhui, 2020. "Analysis and Circuit Implementation of Fractional Order Multi-wing Hidden Attractors," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Yin, Linfei & Wang, Tao & Zheng, Baomin, 2021. "Analytical adaptive distributed multi-objective optimization algorithm for optimal power flow problems," Energy, Elsevier, vol. 216(C).
    3. Ghosh, Mousam & Ghosh, Swarnankur & Ghosh, Suman & Panda, Goutam Kumar & Saha, Pradip Kumar, 2021. "Dynamic model of infected population due to spreading of pandemic COVID-19 considering both intra and inter zone mobilization factors with rate of detection," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Yu, Xihong & Bao, Han & Chen, Mo & Bao, Bocheng, 2023. "Energy balance via memristor synapse in Morris-Lecar two-neuron network with FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    5. Zhang, Jingrui & Li, Zhuoyun & Wang, Beibei, 2021. "Within-day rolling optimal scheduling problem for active distribution networks by multi-objective evolutionary algorithm based on decomposition integrating with thought of simulated annealing," Energy, Elsevier, vol. 223(C).
    6. Barman, Dipesh & Roy, Jyotirmoy & Alrabaiah, Hussam & Panja, Prabir & Mondal, Sankar Prasad & Alam, Shariful, 2021. "Impact of predator incited fear and prey refuge in a fractional order prey predator model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    7. Arunodaya Raj Mishra & Pratibha Rani & Fausto Cavallaro & Ibrahim M. Hezam, 2023. "An IVIF-Distance Measure and Relative Closeness Coefficient-Based Model for Assessing the Sustainable Development Barriers to Biofuel Enterprises in India," Sustainability, MDPI, vol. 15(5), pages 1-22, February.
    8. Li, Tao, 2022. "Analyst's stock views and revision actions," Finance Research Letters, Elsevier, vol. 44(C).
    9. Bukh, A.V. & Kashtanova, S.V. & Shepelev, I.A., 2023. "Complex error minimization algorithm with adaptive change rate," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    10. Yan, Lisha & Wang, Zhen & Zhang, Mingguang & Fan, Yingjie, 2023. "Sampled-data control for mean-square exponential stabilization of memristive neural networks under deception attacks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    11. Bozkurt, Fatma & Yousef, Ali & Baleanu, Dumitru & Alzabut, Jehad, 2020. "A mathematical model of the evolution and spread of pathogenic coronaviruses from natural host to human host," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    12. Li, Shiying & Xu, Jun & Gao, Haonan & Tao, Tao & Mei, Xuesong, 2020. "Safety probability based multi-objective optimization of energy-harvesting suspension system," Energy, Elsevier, vol. 209(C).
    13. Saeed Nosratabadi & Amir Mosavi & Puhong Duan & Pedram Ghamisi, 2020. "Data Science in Economics," Papers 2003.13422, arXiv.org.
    14. Zhang, Boyi & Shang, Pengjian & Zhou, Qin, 2021. "The identification of fractional order systems by multiscale multivariate analysis," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    15. Chen, Xi & Yu, Ruyi & Ullah, Sajid & Wu, Dianming & Li, Zhiqiang & Li, Qingli & Qi, Honggang & Liu, Jihui & Liu, Min & Zhang, Yundong, 2022. "A novel loss function of deep learning in wind speed forecasting," Energy, Elsevier, vol. 238(PB).
    16. Aggarwal, Divya & Chandrasekaran, Shabana & Annamalai, Balamurugan, 2020. "A complete empirical ensemble mode decomposition and support vector machine-based approach to predict Bitcoin prices," Journal of Behavioral and Experimental Finance, Elsevier, vol. 27(C).
    17. Kashkynbayev, Ardak & Cao, Jinde & Suragan, Durvudkhan, 2021. "Global Lagrange stability analysis of retarded SICNNs," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    18. Zhao, Xinxing & Li, Kainan & Ang, Candice Ke En & Ho, Andrew Fu Wah & Liu, Nan & Ong, Marcus Eng Hock & Cheong, Kang Hao, 2022. "A deep learning architecture for forecasting daily emergency department visits with acuity levels," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    19. Ali, Hegagi Mohamed & Ameen, Ismail Gad, 2021. "Optimal control strategies of a fractional order model for Zika virus infection involving various transmissions," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    20. Navarkar, Abhishek & Hasti, Veeraraghava Raju & Deneke, Elihu & Gore, Jay P., 2020. "A data-driven model for thermodynamic properties of a steam generator under cycling operation," Energy, Elsevier, vol. 211(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:chsofr:v:136:y:2020:i:c:s0960077920301922. 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.