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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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |