Rank One Strange Attractors in Periodically Kicked Lorenz System with Time-Delay
Rank one strange attractor in periodically kicked Lorenz system with time-delay is investigated. Our discussion is based on the theory of rank one maps formulated by Wang and Young. First, we develop the rank one chaotic theory to delayed systems. It is shown that strange attractors occur when perio...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/915614 |
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| _version_ | 1832550063018082304 |
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| author | Wenjie Yang Yiping Lin Yunxian Dai |
| author_facet | Wenjie Yang Yiping Lin Yunxian Dai |
| author_sort | Wenjie Yang |
| collection | DOAJ |
| description | Rank one strange attractor in periodically kicked Lorenz system with time-delay is investigated. Our discussion is based on the theory of rank one maps formulated by Wang and Young. First, we develop the rank one chaotic
theory to delayed systems. It is shown that strange attractors occur when periodically kicked delayed system undergoes a
generic Hopf bifurcation. Then we use the theory to the periodically kicked Lorenz system with delay, and derivation of conditions
for Hopf bifurcation and rank one chaos along with the results of numerical simulations are presented. |
| format | Article |
| id | doaj-art-5350f2e37947444d8881051491fcf412 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-5350f2e37947444d8881051491fcf4122025-02-03T06:07:47ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/915614915614Rank One Strange Attractors in Periodically Kicked Lorenz System with Time-DelayWenjie Yang0Yiping Lin1Yunxian Dai2Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650500, ChinaDepartment of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650500, ChinaDepartment of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650500, ChinaRank one strange attractor in periodically kicked Lorenz system with time-delay is investigated. Our discussion is based on the theory of rank one maps formulated by Wang and Young. First, we develop the rank one chaotic theory to delayed systems. It is shown that strange attractors occur when periodically kicked delayed system undergoes a generic Hopf bifurcation. Then we use the theory to the periodically kicked Lorenz system with delay, and derivation of conditions for Hopf bifurcation and rank one chaos along with the results of numerical simulations are presented.http://dx.doi.org/10.1155/2015/915614 |
| spellingShingle | Wenjie Yang Yiping Lin Yunxian Dai Rank One Strange Attractors in Periodically Kicked Lorenz System with Time-Delay Discrete Dynamics in Nature and Society |
| title | Rank One Strange Attractors in Periodically Kicked Lorenz System with Time-Delay |
| title_full | Rank One Strange Attractors in Periodically Kicked Lorenz System with Time-Delay |
| title_fullStr | Rank One Strange Attractors in Periodically Kicked Lorenz System with Time-Delay |
| title_full_unstemmed | Rank One Strange Attractors in Periodically Kicked Lorenz System with Time-Delay |
| title_short | Rank One Strange Attractors in Periodically Kicked Lorenz System with Time-Delay |
| title_sort | rank one strange attractors in periodically kicked lorenz system with time delay |
| url | http://dx.doi.org/10.1155/2015/915614 |
| work_keys_str_mv | AT wenjieyang rankonestrangeattractorsinperiodicallykickedlorenzsystemwithtimedelay AT yipinglin rankonestrangeattractorsinperiodicallykickedlorenzsystemwithtimedelay AT yunxiandai rankonestrangeattractorsinperiodicallykickedlorenzsystemwithtimedelay |