A Fractional-Order Discrete Lorenz Map
In this paper, a discrete Lorenz map with the fractional difference is analyzed. Bifurcations of the map in commensurate-order and incommensurate-order cases are studied when an order and a parameter are varied. Hopf bifurcation and periodic-doubling cascade are found by the numerical simulations. T...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2022/2881207 |
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| author | Yanyun Xie |
| author_facet | Yanyun Xie |
| author_sort | Yanyun Xie |
| collection | DOAJ |
| description | In this paper, a discrete Lorenz map with the fractional difference is analyzed. Bifurcations of the map in commensurate-order and incommensurate-order cases are studied when an order and a parameter are varied. Hopf bifurcation and periodic-doubling cascade are found by the numerical simulations. The parameter values of Hopf bifurcation points are determined when the order is taken as a different value. It can be concluded that the parameter decreases as the order increases. Chaos control and synchronization for the fractional-order discrete Lorenz map are studied through designing the suitable controllers. The effectiveness of the controllers is illustrated by numerical simulations. |
| format | Article |
| id | doaj-art-229e818f7fb2417ba6a60a5578676fc1 |
| institution | Kabale University |
| issn | 1687-9139 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-229e818f7fb2417ba6a60a5578676fc12025-02-03T01:20:06ZengWileyAdvances in Mathematical Physics1687-91392022-01-01202210.1155/2022/2881207A Fractional-Order Discrete Lorenz MapYanyun Xie0School of General EducationIn this paper, a discrete Lorenz map with the fractional difference is analyzed. Bifurcations of the map in commensurate-order and incommensurate-order cases are studied when an order and a parameter are varied. Hopf bifurcation and periodic-doubling cascade are found by the numerical simulations. The parameter values of Hopf bifurcation points are determined when the order is taken as a different value. It can be concluded that the parameter decreases as the order increases. Chaos control and synchronization for the fractional-order discrete Lorenz map are studied through designing the suitable controllers. The effectiveness of the controllers is illustrated by numerical simulations.http://dx.doi.org/10.1155/2022/2881207 |
| spellingShingle | Yanyun Xie A Fractional-Order Discrete Lorenz Map Advances in Mathematical Physics |
| title | A Fractional-Order Discrete Lorenz Map |
| title_full | A Fractional-Order Discrete Lorenz Map |
| title_fullStr | A Fractional-Order Discrete Lorenz Map |
| title_full_unstemmed | A Fractional-Order Discrete Lorenz Map |
| title_short | A Fractional-Order Discrete Lorenz Map |
| title_sort | fractional order discrete lorenz map |
| url | http://dx.doi.org/10.1155/2022/2881207 |
| work_keys_str_mv | AT yanyunxie afractionalorderdiscretelorenzmap AT yanyunxie fractionalorderdiscretelorenzmap |