The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE sets
In this paper, we study some chaotic properties of s-dimensional dynamical system of the form Ψa1,a2,…,as=gsas,g1a1,…,gs−1as−1, where ak∈Hk for any k∈1,2,…,s, s≥2 is an integer, and Hk is a compact subinterval of the real line ℝ=−∞,+∞ for any k∈1,2,…,s. Particularly, a necessary and sufficient condi...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/9379628 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850172830601183232 |
|---|---|
| author | Risong Li Tianxiu Lu |
| author_facet | Risong Li Tianxiu Lu |
| author_sort | Risong Li |
| collection | DOAJ |
| description | In this paper, we study some chaotic properties of s-dimensional dynamical system of the form Ψa1,a2,…,as=gsas,g1a1,…,gs−1as−1, where ak∈Hk for any k∈1,2,…,s, s≥2 is an integer, and Hk is a compact subinterval of the real line ℝ=−∞,+∞ for any k∈1,2,…,s. Particularly, a necessary and sufficient condition for a cyclic permutation map Ψa1,a2,…,as=gsas,g1a1,…,gs−1as−1 to be LY-chaotic or h-chaotic or RT-chaotic or D-chaotic is obtained. Moreover, the LY-chaoticity, h-chaoticity, RT-chaoticity, and D-chaoticity of such a cyclic permutation map is explored. Also, we proved that the topological entropy hΨ of such a cyclic permutation map is the same as the topological entropy of each of the following maps: gj∘gj−1∘⋯∘g1l∘gs∘gs−1∘⋯∘gj+1, if j=1,…,s−1and gs∘gs−1∘⋯∘g1, and that Ψ is sensitive if and only if at least one of the coordinates maps of Ψs is sensitive. |
| format | Article |
| id | doaj-art-d4cdf103edd5408185eb43753e4575a9 |
| institution | OA Journals |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-d4cdf103edd5408185eb43753e4575a92025-08-20T02:19:58ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/93796289379628The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE setsRisong Li0Tianxiu Lu1School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, ChinaCollege of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, ChinaIn this paper, we study some chaotic properties of s-dimensional dynamical system of the form Ψa1,a2,…,as=gsas,g1a1,…,gs−1as−1, where ak∈Hk for any k∈1,2,…,s, s≥2 is an integer, and Hk is a compact subinterval of the real line ℝ=−∞,+∞ for any k∈1,2,…,s. Particularly, a necessary and sufficient condition for a cyclic permutation map Ψa1,a2,…,as=gsas,g1a1,…,gs−1as−1 to be LY-chaotic or h-chaotic or RT-chaotic or D-chaotic is obtained. Moreover, the LY-chaoticity, h-chaoticity, RT-chaoticity, and D-chaoticity of such a cyclic permutation map is explored. Also, we proved that the topological entropy hΨ of such a cyclic permutation map is the same as the topological entropy of each of the following maps: gj∘gj−1∘⋯∘g1l∘gs∘gs−1∘⋯∘gj+1, if j=1,…,s−1and gs∘gs−1∘⋯∘g1, and that Ψ is sensitive if and only if at least one of the coordinates maps of Ψs is sensitive.http://dx.doi.org/10.1155/2020/9379628 |
| spellingShingle | Risong Li Tianxiu Lu The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE sets Complexity |
| title | The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE sets |
| title_full | The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE sets |
| title_fullStr | The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE sets |
| title_full_unstemmed | The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE sets |
| title_short | The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE sets |
| title_sort | topological entropy of cyclic permutation maps and some chaotic properties on their mpe sets |
| url | http://dx.doi.org/10.1155/2020/9379628 |
| work_keys_str_mv | AT risongli thetopologicalentropyofcyclicpermutationmapsandsomechaoticpropertiesontheirmpesets AT tianxiulu thetopologicalentropyofcyclicpermutationmapsandsomechaoticpropertiesontheirmpesets AT risongli topologicalentropyofcyclicpermutationmapsandsomechaoticpropertiesontheirmpesets AT tianxiulu topologicalentropyofcyclicpermutationmapsandsomechaoticpropertiesontheirmpesets |