This paper establishes several criteria for strong Li–Yorke chaos and distributional chaos in non-autonomous discrete dynamical systems. The main criterion of distributional δ-chaos for some δ>0 is induced by weak A-coupled-expansion in a sequence of nonempty compact subsets, where A is an irreducible transition matrix with at least one row sum larger than 1. Some of these results not only extend the existing related results for autonomous discrete systems to non-autonomous discrete systems, but also relax the assumptions of the counterparts. One example of a non-autonomous logistic system is provided for illustration.
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