Different dimensional fractional-order discrete chaotic systems based on the Caputo h-difference discrete operator: dynamics, control, and synchronization
Abstract The paper investigates control and synchronization of fractional-order maps described by the Caputo h-difference operator. At first, two new fractional maps are introduced, i.e., the Two-Dimensional Fractional-order Lorenz Discrete System (2D-FoLDS) and Three-Dimensional Fractional-order Wa...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-11-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-03086-x |
| _version_ | 1818192372116226048 |
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| author | Ibtissem Talbi Adel Ouannas Amina-Aicha Khennaoui Abdelhak Berkane Iqbal M. Batiha Giuseppe Grassi Viet-Thanh Pham |
| author_facet | Ibtissem Talbi Adel Ouannas Amina-Aicha Khennaoui Abdelhak Berkane Iqbal M. Batiha Giuseppe Grassi Viet-Thanh Pham |
| author_sort | Ibtissem Talbi |
| collection | DOAJ |
| description | Abstract The paper investigates control and synchronization of fractional-order maps described by the Caputo h-difference operator. At first, two new fractional maps are introduced, i.e., the Two-Dimensional Fractional-order Lorenz Discrete System (2D-FoLDS) and Three-Dimensional Fractional-order Wang Discrete System (3D-FoWDS). Then, some novel theorems based on the Lyapunov approach are proved, with the aim of controlling and synchronizing the map dynamics. In particular, a new hybrid scheme is proposed, which enables synchronization to be achieved between a master system based on a 2D-FoLDS and a slave system based on a 3D-FoWDS. Simulation results are reported to highlight the effectiveness of the conceived approach. |
| first_indexed | 2024-12-12T00:29:27Z |
| format | Article |
| id | doaj.art-3e40421581a544809ba976971547909f |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-12T00:29:27Z |
| publishDate | 2020-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-3e40421581a544809ba976971547909f2022-12-22T00:44:31ZengSpringerOpenAdvances in Difference Equations1687-18472020-11-012020111510.1186/s13662-020-03086-xDifferent dimensional fractional-order discrete chaotic systems based on the Caputo h-difference discrete operator: dynamics, control, and synchronizationIbtissem Talbi0Adel Ouannas1Amina-Aicha Khennaoui2Abdelhak Berkane3Iqbal M. Batiha4Giuseppe Grassi5Viet-Thanh Pham6Department of Mathematics, University of ConstantineDepartment of Mathematics and Computer Science, University of Larbi Ben M’hidiLaboratory of Dynamical Systems and Control, University of Larbi Ben M’hidiDepartment of Mathematics, University of ConstantineDepartment of Mathematics, Faculty of Science, University of JordanDipartimento Ingegneria Innovazione, Universita del SalentoNonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang UniversityAbstract The paper investigates control and synchronization of fractional-order maps described by the Caputo h-difference operator. At first, two new fractional maps are introduced, i.e., the Two-Dimensional Fractional-order Lorenz Discrete System (2D-FoLDS) and Three-Dimensional Fractional-order Wang Discrete System (3D-FoWDS). Then, some novel theorems based on the Lyapunov approach are proved, with the aim of controlling and synchronizing the map dynamics. In particular, a new hybrid scheme is proposed, which enables synchronization to be achieved between a master system based on a 2D-FoLDS and a slave system based on a 3D-FoWDS. Simulation results are reported to highlight the effectiveness of the conceived approach.http://link.springer.com/article/10.1186/s13662-020-03086-xDiscrete fractional calculusControlSynchronizationDiscrete Lorenz systemDiscrete Wang systemLyapunov approach |
| spellingShingle | Ibtissem Talbi Adel Ouannas Amina-Aicha Khennaoui Abdelhak Berkane Iqbal M. Batiha Giuseppe Grassi Viet-Thanh Pham Different dimensional fractional-order discrete chaotic systems based on the Caputo h-difference discrete operator: dynamics, control, and synchronization Advances in Difference Equations Discrete fractional calculus Control Synchronization Discrete Lorenz system Discrete Wang system Lyapunov approach |
| title | Different dimensional fractional-order discrete chaotic systems based on the Caputo h-difference discrete operator: dynamics, control, and synchronization |
| title_full | Different dimensional fractional-order discrete chaotic systems based on the Caputo h-difference discrete operator: dynamics, control, and synchronization |
| title_fullStr | Different dimensional fractional-order discrete chaotic systems based on the Caputo h-difference discrete operator: dynamics, control, and synchronization |
| title_full_unstemmed | Different dimensional fractional-order discrete chaotic systems based on the Caputo h-difference discrete operator: dynamics, control, and synchronization |
| title_short | Different dimensional fractional-order discrete chaotic systems based on the Caputo h-difference discrete operator: dynamics, control, and synchronization |
| title_sort | different dimensional fractional order discrete chaotic systems based on the caputo h difference discrete operator dynamics control and synchronization |
| topic | Discrete fractional calculus Control Synchronization Discrete Lorenz system Discrete Wang system Lyapunov approach |
| url | http://link.springer.com/article/10.1186/s13662-020-03086-x |
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