Let (X, F) be a set-valued dynamical system, where X is a compact metric space and F: Xto 2Xsetminus∅is a set-valued map. We introduce the notions of Xiong chaos, strong Xiong chaos, weak mixing, and distributional chaos for set-valued dynamical systems. We show that Xiong chaos and weak mixing are equivalent, and that strong Xiong chaos sets are distributional chaos in a sequence.
Xingfu et al. (Thu,) studied this question.