Sequence of Routes to Chaos in a Lorenz-Type System
This paper reports a new bifurcation pattern observed in a Lorenz-type system. The pattern is composed of a main bifurcation route to chaos (n=1) and a sequence of sub-bifurcation routes with n=3,4,5,…,14 isolated sub-branches to chaos. When n is odd, the n isolated sub-branches are from a period-n...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/3162170 |
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| author | Fangyan Yang Yongming Cao Lijuan Chen Qingdu Li |
| author_facet | Fangyan Yang Yongming Cao Lijuan Chen Qingdu Li |
| author_sort | Fangyan Yang |
| collection | DOAJ |
| description | This paper reports a new bifurcation pattern observed in a Lorenz-type system. The pattern is composed of a main bifurcation route to chaos (n=1) and a sequence of sub-bifurcation routes with n=3,4,5,…,14 isolated sub-branches to chaos. When n is odd, the n isolated sub-branches are from a period-n limit cycle, followed by twin period-n limit cycles via a pitchfork bifurcation, twin chaotic attractors via period-doubling bifurcations, and a symmetric chaotic attractor via boundary crisis. When n is even, the n isolated sub-branches are from twin period-n/2 limit cycles, which become twin chaotic attractors via period-doubling bifurcations. The paper also shows that the main route and the sub-routes can coexist peacefully by studying basins of attraction. |
| format | Article |
| id | doaj-art-82abd96cf4cd4f70988513645e7696d4 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-82abd96cf4cd4f70988513645e7696d42025-02-03T06:46:07ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/31621703162170Sequence of Routes to Chaos in a Lorenz-Type SystemFangyan Yang0Yongming Cao1Lijuan Chen2Qingdu Li3School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, ChinaChongqing Key Laboratory of Complex Systems and Bionic Control, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaSchool of Mathematical Science, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, ChinaChongqing Key Laboratory of Complex Systems and Bionic Control, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaThis paper reports a new bifurcation pattern observed in a Lorenz-type system. The pattern is composed of a main bifurcation route to chaos (n=1) and a sequence of sub-bifurcation routes with n=3,4,5,…,14 isolated sub-branches to chaos. When n is odd, the n isolated sub-branches are from a period-n limit cycle, followed by twin period-n limit cycles via a pitchfork bifurcation, twin chaotic attractors via period-doubling bifurcations, and a symmetric chaotic attractor via boundary crisis. When n is even, the n isolated sub-branches are from twin period-n/2 limit cycles, which become twin chaotic attractors via period-doubling bifurcations. The paper also shows that the main route and the sub-routes can coexist peacefully by studying basins of attraction.http://dx.doi.org/10.1155/2020/3162170 |
| spellingShingle | Fangyan Yang Yongming Cao Lijuan Chen Qingdu Li Sequence of Routes to Chaos in a Lorenz-Type System Discrete Dynamics in Nature and Society |
| title | Sequence of Routes to Chaos in a Lorenz-Type System |
| title_full | Sequence of Routes to Chaos in a Lorenz-Type System |
| title_fullStr | Sequence of Routes to Chaos in a Lorenz-Type System |
| title_full_unstemmed | Sequence of Routes to Chaos in a Lorenz-Type System |
| title_short | Sequence of Routes to Chaos in a Lorenz-Type System |
| title_sort | sequence of routes to chaos in a lorenz type system |
| url | http://dx.doi.org/10.1155/2020/3162170 |
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