This paper studies distributional chaos in non-autonomous discrete systemsgenerated by given sequences of maps in metric spaces. In the case that themetric space is compact, it is shown that a system is Li-Yorke{\delta}-chaoticif and only if it is distributionally{\delta}'-chaotic in a sequence; and threecriteria of distributional {\delta}-chaos are established, which are caused bytopologically weak mixing, asymptotic average shadowing property, and someexpanding condition, respectively, where {\delta} and {\delta}' are positiveconstants. In a general case, a criterion of distributional chaos in a sequenceinduced by a Xiong chaotic set is established.
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