Chapter

Advances in Computer Science, Intelligent System and Environment

Volume 105 of the series Advances in Intelligent and Soft Computing pp 269-275

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

  • Lidong WangAffiliated withSchool of Science, Dalian Nationalities UniversitySchool of Information and Computing Science, Beifang University of Nationality
  • , Yuelin GaoAffiliated withSchool of Information and Computing Science, Beifang University of Nationality
  • , Wing-Kuen LingAffiliated withSchool of Engineering, University of Lincoln

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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).

Keywords

Set-valued discrete systems distributional chaos in a sequence periodic points Hausdorff metric