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On distributional chaos in non-autonomous discrete systems

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  • Shao, Hua
  • Shi, Yuming
  • Zhu, Hao

Abstract

This paper studies distributional chaos in non-autonomous discrete systems generated by given sequences of maps in metric spaces. In the case that the metric space is compact, it is shown that a system is Li–Yorke δ-chaotic if and only if it is distributionally δ′-chaotic in a sequence; and three criteria of distributional δ-chaos are established, which are caused by topologically weak mixing, asymptotic average shadowing property, and some expanding condition, respectively, where δ and δ′ are positive constants. In a general case, a criterion of distributional chaos in a sequence induced by a Xiong chaotic set is established.

Suggested Citation

  • Shao, Hua & Shi, Yuming & Zhu, Hao, 2018. "On distributional chaos in non-autonomous discrete systems," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 234-243.
    • Handle: RePEc:eee:chsofr:v:107:y:2018:i:c:p:234-243
    DOI: 10.1016/j.chaos.2018.01.005
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    References listed on IDEAS

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    1. Tian, Chuanjun & Chen, Guanrong, 2006. "Chaos of a sequence of maps in a metric space," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1067-1075.
    2. Balibrea, F. & Smı́tal, J. & Štefánková, M., 2005. "The three versions of distributional chaos," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1581-1583.
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    Cited by:

    1. Anguiano-Gijón, Carlos Alberto & Muñoz-Vázquez, Aldo Jonathan & Sánchez-Torres, Juan Diego & Romero-Galván, Gerardo & Martínez-Reyes, Fernando, 2019. "On predefined-time synchronisation of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 172-178.
    2. Salman, Mohammad & Das, Ruchi, 2018. "Multi-sensitivity and other stronger forms of sensitivity in non-autonomous discrete systems," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 341-348.

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