On distributional chaos in non-autonomous discrete systems

Hua Shao, Yuming Shi and Hao Zhu

Chaos, Solitons & Fractals, 2018, vol. 107, issue C, 234-243

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.

Keywords: Non-autonomous discrete system; Distributional chaos; Li–Yorke chaos; Topologically weak mixing; Shadowing property (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:107:y:2018:i:c:p:234-243

DOI: 10.1016/j.chaos.2018.01.005

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