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

  • Lidong Wang
  • Yuelin Gao
  • Wing-Kuen Ling
Conference paper

DOI: 10.1007/978-3-642-23756-0_44

Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 105)
Cite this paper as:
Wang L., Gao Y., Ling WK. (2011) Research on Chaos Caused by a Transitive Map Based on Intelligent Materials. In: Jin D., Lin S. (eds) Advances in Computer Science, Intelligent System and Environment. Advances in Intelligent and Soft Computing, vol 105. Springer, Berlin, Heidelberg

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 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Lidong Wang
    • 1
    • 2
  • Yuelin Gao
    • 2
  • Wing-Kuen Ling
    • 3
  1. 1.School of ScienceDalian Nationalities UniversityDalianPR China
  2. 2.School of Information and Computing ScienceBeifang University of NationalityYinchuanPR China
  3. 3.School of EngineeringUniversity of LincolnLincolnUnited Kingdom

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