Research on Chaos Caused by a Transitive Map Based on Intelligent Materials

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Abstract

Let (X, d) be a compact metric space, and ( $\mathcal{K}$ (X),H) is d induced Hausdorff metric space of all non-empty compact subsets of X. In the paper, we investigated the distributional chaoticity in a sequence of discrete dynamical system (X, f) and the distributional chaoticity in a sequence of set-valued discrete system ( $\mathcal{K}$ (X),). And we gave a sufficient condition about the existence of distributionally chaotic sets in a sequence in discrete system (X, f) and discrete dynamical system ( $\mathcal{K}$ , H).