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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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).
    3. 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.
    4. 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.
    5. Qin, Shijie & Liao, Shijun, 2020. "Influence of numerical noises on computer-generated simulation of spatio-temporal chaos," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    6. Ma, Wen-Xiu, 2009. "Multi-component bi-Hamiltonian Dirac integrable equations," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 282-287.
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