Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 67908, 10 pages
Horseshoe in a class of planar mappings
1Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China
2Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Received 6 March 2005; Accepted 2 June 2005
Copyright © 2006 Yan Huang and Xiao-Song Yang. 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.
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 , , and with different parameters, we study their powers , , and . 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 is semiconjugate to the 3-shift mapping; the mappings and are semiconjugate to the 4-shift mapping.