- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 875381, 9 pages
Some Chaotic Properties of Discrete Fuzzy Dynamical Systems
1College of Computer Science, Chongqing University, Chongqing 401331, China
2College of Applied Mathematics, Hunan University, Changsha 410082, Hunan, China
3Department of Mathematics and Finance, Chongqing University of Arts and Sciences, Yongchuan 402160, China
Received 16 September 2012; Revised 21 November 2012; Accepted 21 November 2012
Academic Editor: Gani Stamov
Copyright © 2012 Yaoyao Lan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- H. Román-Flores, “A note on transitivity in set-valued discrete systems,” Chaos, Solitons and Fractals, vol. 17, no. 1, pp. 99–104, 2003.
- A. Fedeli, “On chaotic set-valued discrete dynamical systems,” Chaos, Solitons and Fractals, vol. 23, no. 4, pp. 1381–1384, 2005.
- A. Peris, “Set-valued discrete chaos,” Chaos, Solitons and Fractals, vol. 26, no. 1, pp. 19–23, 2005.
- J. Banks, “Chaos for induced hyperspace maps,” Chaos, Solitons and Fractals, vol. 25, no. 3, pp. 681–685, 2005.
- Y. Wang, G. Wei, and W. H. Campbell, “Sensitive dependence on initial conditions between dynamical systems and their induced hyperspace dynamical systems,” Topology and Its Applications, vol. 156, no. 4, pp. 803–811, 2009.
- R. Gu, “Kato's chaos in set-valued discrete systems,” Chaos, Solitons and Fractals, vol. 31, no. 3, pp. 765–771, 2007.
- H. Román-Flores and Y. Chalco-Cano, “Some chaotic properties of Zadeh's extensions,” Chaos, Solitons and Fractals, vol. 35, no. 3, pp. 452–459, 2008.
- J. Kupka, “On Devaney chaotic induced fuzzy and set-valued dynamical systems,” Fuzzy Sets and Systems, vol. 177, pp. 34–44, 2011.
- J. Kupka, “On fuzzifications of discrete dynamical systems,” Information Sciences, vol. 181, no. 13, pp. 2858–2872, 2011.
- J. Kupka, “Some chaotic and mixing properties of Zadeh's Extension,” in Proceedings of the International Fuzzy Systems Association World Congress and European Society of Fuzzy Logic and Technology Conference, pp. 589–594, 2009.
- P. Diamond and P. Kloeden, “Characterization of compact subsets of fuzzy sets,” Fuzzy Sets and Systems, vol. 29, no. 3, pp. 341–348, 1989.
- O. Kaleva, “On the convergence of fuzzy sets,” Fuzzy Sets and Systems, vol. 17, no. 1, pp. 53–65, 1985.
- R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley Studies in Nonlinearity, Addison-Wesley, New York, NY, USA, 2nd edition, 1989.
- J. Banks, J. Brooks, G. Cairns, G. Davis, and P. Stacey, “On Devaney's definition of chaos,” The American Mathematical Monthly, vol. 99, no. 4, pp. 332–334, 1992.
- S. Silverman, “On maps with dense orbits and the definition of chaos,” The Rocky Mountain Journal of Mathematics, vol. 22, no. 1, pp. 353–375, 1992.
- P. Diamond and A. Pokrovskii, “Chaos, entropy and a generalized extension principle,” Fuzzy Sets and Systems, vol. 61, no. 3, pp. 277–283, 1994.