IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v167y2023ics0960077922012164.html
   My bibliography  Save this article

Ultra-chaos of a mobile robot: A higher disorder than normal-chaos

Author

Listed:
  • Yang, Yu
  • Qin, Shijie
  • Liao, Shijun

Abstract

The trajectory of a chaotic dynamical system is sensitive to the initial condition, while its statistics normally do not have sensitive dependence on small disturbances. Such a kind of chaos is called normal-chaos. Recently, a new concept named ultra-chaos has been proposed for the first time. Unlike normal-chaos, the small disturbances lead to large deviation even in statistics for ultra-chaos. However, few ultra-chaos have been reported up to now. In this work, we investigate the influences of small disturbances on the chaotic navigation system and the motion of mobile robot, respectively. It is illustrated that the chaotic navigation system of the mobile robot belongs to normal-chaos. However, the motion of chaotic mobile robot belongs to ultra-chaos. Tiny disturbances would cause huge deviation in the motion of chaotic mobile robot, even in the statistical meaning. Thus, the ultra-chaos is indeed a higher-level disorder compared with the normal-chaos and it widely exists in practice. Hopefully, the new concept, i.e., ultra-chaos, could deepen our understandings of chaos and open a new door to explore chaos theory.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922012164
    DOI: 10.1016/j.chaos.2022.113037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922012164
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.113037?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. Nwachioma, Christian & Pérez-Cruz, J. Humberto, 2021. "Analysis of a new chaotic system, electronic realization and use in navigation of differential drive mobile robot," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Ma, Wen-Xiu, 2009. "Multi-component bi-Hamiltonian Dirac integrable equations," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 282-287.
    3. Sheikholeslami, M. & Vajravelu, K., 2017. "Nanofluid flow and heat transfer in a cavity with variable magnetic field," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 272-282.
    4. Nasr, Salah & Mekki, Hassen & Bouallegue, Kais, 2019. "A multi-scroll chaotic system for a higher coverage path planning of a mobile robot using flatness controller," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 366-375.
    5. Luiz S. Martins-Filho & Elbert E. N. Macau, 2007. "Patrol Mobile Robots and Chaotic Trajectories," Mathematical Problems in Engineering, Hindawi, vol. 2007, pages 1-13, June.
    6. Qin, Shijie & Liao, Shijun, 2020. "Influence of numerical noises on computer-generated simulation of spatio-temporal chaos," Chaos, Solitons & Fractals, Elsevier, vol. 136(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. Lazaros Moysis & Karthikeyan Rajagopal & Aleksandra V. Tutueva & Christos Volos & Beteley Teka & Denis N. Butusov, 2021. "Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map," Mathematics, MDPI, vol. 9(15), pages 1-16, August.
    2. Manh, Tran Dinh & Jafaryar, M. & Hamad, Samir Mustafa & Barzinjy, Azeez A. & Shafee, Ahmad & Abohamzeh, Elham & Tlili, Iskander, 2020. "Nanoparticles hydrothermal simulation in a pipe with insertion of compound turbulator analyzing entropy generation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    3. Cheng, Guanghui & Li, Dan & Yao, Yuangen & Gui, Rong, 2023. "Multi-scroll chaotic attractors with multi-wing via oscillatory potential wells," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Dlamini, A. & Doungmo Goufo, E.F., 2023. "Generation of self-similarity in a chaotic system of attractors with many scrolls and their circuit’s implementation," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    5. Xiong, Qingang & Ayani, M. & Barzinjy, Azeez A. & Dara, Rebwar Nasir & Shafee, Ahmad & Nguyen-Thoi, Trung, 2020. "Modeling of heat transfer augmentation due to complex-shaped turbulator using nanofluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    6. 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).
    7. Ali Rehman & Zabidin Salleh, 2021. "Influence of Marangoni Convection on Magnetohydrodynamic Viscous Dissipation and Heat Transfer on Hybrid Nanofluids in a Rotating System among Two Surfaces," Mathematics, MDPI, vol. 9(18), pages 1-16, September.
    8. Manh, Tran Dinh & Nam, Nguyen Dang & Jacob, Kavikumar & Hajizadeh, Ahmad & Babazadeh, Houman & Mahjoub, Mohammed & Tlili, I. & Li, Z., 2020. "Simulation of heat transfer in 2D porous tank in appearance of magnetic nanofluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    9. Zhang, Jie & Zuo, Jiangang & Wang, Meng & Guo, Yan & Xie, Qinggang & Hou, Jinyou, 2024. "Design and application of multiscroll chaotic attractors based on a novel multi-segmented memristor," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    10. Ali, Bagh & Khan, Shahid Ali & Hussein, Ahmed Kadhim & Thumma, Thirupathi & Hussain, Sajjad, 2022. "Hybrid nanofluids: Significance of gravity modulation, heat source/ sink, and magnetohydrodynamic on dynamics of micropolar fluid over an inclined surface via finite element simulation," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    11. Manh, Tran Dinh & Khan, Ahmad Raza & Shafee, Ahmad & Nam, Nguyen Dang & Tlili, I. & Nguyen-Thoi, Trung & Li, Z., 2020. "Hybrid nanoparticles migration due to MHD free convection considering radiation effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    12. Izadi, Mohsen & Mohebbi, Rasul & Sajjadi, Hasan & Delouei, Amin Amiri, 2019. "LTNE modeling of Magneto-Ferro natural convection inside a porous enclosure exposed to nonuniform magnetic field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    13. Manh, Tran Dinh & Nam, Nguyen Dang & Abdulrahman, Gihad Keyany & Khan, Muhammad Humran & Tlili, I. & Shafee, Ahmad & Shamlooei, M. & Nguyen-Thoi, Trung, 2020. "Investigation of hybrid nanofluid migration within a porous closed domain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    14. Atangana, Abdon & Bouallegue, Ghaith & Bouallegue, Kais, 2020. "New multi-scroll attractors obtained via Julia set mapping," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    15. Shafee, Ahmad & Muhammad, Taseer & Alsakran, Reem & Tlili, Iskander & Babazadeh, Houman & Khan, Umar, 2020. "Numerical examination for nanomaterial forced convection within a permeable cavity involving magnetic forces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    16. Manh, Tran Dinh & Tlili, I. & Shafee, Ahmad & Nguyen-Thoi, Trung & Hamouda, Hassen, 2020. "Modeling of hybrid nanofluid behavior within a permeable media involving buoyancy effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    17. Minati, Ludovico & Frasca, Mattia & Valdes-Sosa, Pedro A. & Barbot, Jean-Pierre & Letellier, Christophe, 2023. "Flatness-based real-time control of experimental analog chaotic oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    18. Nwachioma, Christian & Pérez-Cruz, J. Humberto, 2021. "Analysis of a new chaotic system, electronic realization and use in navigation of differential drive mobile robot," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    19. Xiong, Qingang & Tlili, I. & Dara, Rebwar Nasir & Shafee, Ahmad & Nguyen-Thoi, Trung & Rebey, Amor & Haq, Rizwan-ul & Li, Z., 2020. "Energy storage simulation involving NEPCM solidification in appearance of fins," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    20. Yu-Shan Bai & Peng-Xiang Su & Wen-Xiu Ma, 2021. "N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions," Mathematics, MDPI, vol. 9(7), pages 1-13, March.

    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:167:y:2023:i:c:s0960077922012164. 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.