Horseshoe in a class of planar mappings
Bursting dynamics of mappings is investigated in this paper. We first present stability analysis of the mappings' equilibria with various parameters. Then for three mappings P, P¯, and P^ with different parameters, we study their powers P4, P¯6, and P^4. We show that the mappings thus obtained...
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Hindawi Limited
2006-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/DDNS/2006/67908 |
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doaj-b6432b387dd24908a0964991f539fe7b2020-11-24T21:33:59ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2006-01-01200610.1155/DDNS/2006/6790867908Horseshoe in a class of planar mappingsYan Huang0Xiao-Song Yang1Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, ChinaDepartment of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, ChinaBursting dynamics of mappings is investigated in this paper. We first present stability analysis of the mappings' equilibria with various parameters. Then for three mappings P, P¯, and P^ with different parameters, we study their powers P4, P¯6, and P^4. We show that the mappings thus obtained are chaotic by giving a rigorous verification of existence of horseshoes in these mappings. Precisely, we prove that the mapping P¯6 is semiconjugate to the 3-shift mapping; the mappings P4 and P^4 are semiconjugate to the 4-shift mapping.http://dx.doi.org/10.1155/DDNS/2006/67908 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yan Huang Xiao-Song Yang |
| spellingShingle |
Yan Huang Xiao-Song Yang Horseshoe in a class of planar mappings Discrete Dynamics in Nature and Society |
| author_facet |
Yan Huang Xiao-Song Yang |
| author_sort |
Yan Huang |
| title |
Horseshoe in a class of planar mappings |
| title_short |
Horseshoe in a class of planar mappings |
| title_full |
Horseshoe in a class of planar mappings |
| title_fullStr |
Horseshoe in a class of planar mappings |
| title_full_unstemmed |
Horseshoe in a class of planar mappings |
| title_sort |
horseshoe in a class of planar mappings |
| publisher |
Hindawi Limited |
| series |
Discrete Dynamics in Nature and Society |
| issn |
1026-0226 1607-887X |
| publishDate |
2006-01-01 |
| description |
Bursting dynamics of mappings is investigated in this paper. We
first present stability analysis of the mappings' equilibria with
various parameters. Then for three mappings P, P¯, and P^ with different parameters, we study their powers P4, P¯6, and P^4. We show that the mappings thus
obtained are chaotic by giving a rigorous verification of
existence of horseshoes in these mappings. Precisely, we prove
that the mapping P¯6 is semiconjugate to the 3-shift mapping; the mappings P4 and P^4 are semiconjugate to the 4-shift mapping. |
| url |
http://dx.doi.org/10.1155/DDNS/2006/67908 |
| work_keys_str_mv |
AT yanhuang horseshoeinaclassofplanarmappings AT xiaosongyang horseshoeinaclassofplanarmappings |
| _version_ |
1725950950568361984 |