Chaos for Discrete Dynamical System
We prove that a dynamical system is chaotic in the sense of Martelli and Wiggins, when it is a transitive distributively chaotic in a sequence. Then, we give a sufficient condition for the dynamical system to be chaotic in the strong sense of Li-Yorke. We also prove that a dynamical system is distri...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/212036 |
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| _version_ | 1832554335533268992 |
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| author | Lidong Wang Heng Liu Yuelin Gao |
| author_facet | Lidong Wang Heng Liu Yuelin Gao |
| author_sort | Lidong Wang |
| collection | DOAJ |
| description | We prove that a dynamical system is chaotic in the sense of Martelli and Wiggins, when it is a transitive distributively chaotic in a sequence. Then, we give a sufficient condition for the dynamical system to be chaotic in the strong sense of Li-Yorke. We also prove that a dynamical system is distributively chaotic in a sequence, when it is chaotic in the strong sense of Li-Yorke. |
| format | Article |
| id | doaj-art-09c4f32e1ca740c7b640414284f4735a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-09c4f32e1ca740c7b640414284f4735a2025-02-03T05:51:39ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/212036212036Chaos for Discrete Dynamical SystemLidong Wang0Heng Liu1Yuelin Gao2Information and Computational Science department, Beifang University of Nationality, Yinchuan, Ningxia 750021, ChinaInformation and Computational Science department, Beifang University of Nationality, Yinchuan, Ningxia 750021, ChinaInformation and Computational Science department, Beifang University of Nationality, Yinchuan, Ningxia 750021, ChinaWe prove that a dynamical system is chaotic in the sense of Martelli and Wiggins, when it is a transitive distributively chaotic in a sequence. Then, we give a sufficient condition for the dynamical system to be chaotic in the strong sense of Li-Yorke. We also prove that a dynamical system is distributively chaotic in a sequence, when it is chaotic in the strong sense of Li-Yorke.http://dx.doi.org/10.1155/2013/212036 |
| spellingShingle | Lidong Wang Heng Liu Yuelin Gao Chaos for Discrete Dynamical System Journal of Applied Mathematics |
| title | Chaos for Discrete Dynamical System |
| title_full | Chaos for Discrete Dynamical System |
| title_fullStr | Chaos for Discrete Dynamical System |
| title_full_unstemmed | Chaos for Discrete Dynamical System |
| title_short | Chaos for Discrete Dynamical System |
| title_sort | chaos for discrete dynamical system |
| url | http://dx.doi.org/10.1155/2013/212036 |
| work_keys_str_mv | AT lidongwang chaosfordiscretedynamicalsystem AT hengliu chaosfordiscretedynamicalsystem AT yuelingao chaosfordiscretedynamicalsystem |