Fractional Grassi–Miller Map Based on the Caputo h-Difference Operator: Linear Methods for Chaos Control and Synchronization
Investigating dynamic properties of discrete chaotic systems with fractional order has been receiving much attention recently. This paper provides a contribution to the topic by presenting a novel version of the fractional Grassi–Miller map, along with improved schemes for controlling and synchroniz...
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| Main Authors: | , , , , , |
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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/10.1155/2020/8825694 |
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| author | Ibtissem Talbi Adel Ouannas Giuseppe Grassi Amina-Aicha Khennaoui Viet-Thanh Pham Dumitru Baleanu |
| author_facet | Ibtissem Talbi Adel Ouannas Giuseppe Grassi Amina-Aicha Khennaoui Viet-Thanh Pham Dumitru Baleanu |
| author_sort | Ibtissem Talbi |
| collection | DOAJ |
| description | Investigating dynamic properties of discrete chaotic systems with fractional order has been receiving much attention recently. This paper provides a contribution to the topic by presenting a novel version of the fractional Grassi–Miller map, along with improved schemes for controlling and synchronizing its dynamics. By exploiting the Caputo h-difference operator, at first, the chaotic dynamics of the map are analyzed via bifurcation diagrams and phase plots. Then, a novel theorem is proved in order to stabilize the dynamics of the map at the origin by linear control laws. Additionally, two chaotic fractional Grassi–Miller maps are synchronized via linear controllers by utilizing a novel theorem based on a suitable Lyapunov function. Finally, simulation results are reported to show the effectiveness of the approach developed herein. |
| format | Article |
| id | doaj-art-74e3592615924971aebb3f8011b4fee3 |
| 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-74e3592615924971aebb3f8011b4fee32025-02-03T01:28:24ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/88256948825694Fractional Grassi–Miller Map Based on the Caputo h-Difference Operator: Linear Methods for Chaos Control and SynchronizationIbtissem Talbi0Adel Ouannas1Giuseppe Grassi2Amina-Aicha Khennaoui3Viet-Thanh Pham4Dumitru Baleanu5Department of Mathematics, Constantine University, Constantine 25000, AlgeriaDepartment of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi, AlgeriaUniversita del Salento, Dipartimento Ingegneria Innovazione, Lecce 73100, ItalyLaboratory of Dynamical System and Control, University of Larbi Ben M’hidi, Oum El Bouaghi, AlgeriaNonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, VietnamCankaya University, Ankara, TurkeyInvestigating dynamic properties of discrete chaotic systems with fractional order has been receiving much attention recently. This paper provides a contribution to the topic by presenting a novel version of the fractional Grassi–Miller map, along with improved schemes for controlling and synchronizing its dynamics. By exploiting the Caputo h-difference operator, at first, the chaotic dynamics of the map are analyzed via bifurcation diagrams and phase plots. Then, a novel theorem is proved in order to stabilize the dynamics of the map at the origin by linear control laws. Additionally, two chaotic fractional Grassi–Miller maps are synchronized via linear controllers by utilizing a novel theorem based on a suitable Lyapunov function. Finally, simulation results are reported to show the effectiveness of the approach developed herein.http://dx.doi.org/10.1155/2020/8825694 |
| spellingShingle | Ibtissem Talbi Adel Ouannas Giuseppe Grassi Amina-Aicha Khennaoui Viet-Thanh Pham Dumitru Baleanu Fractional Grassi–Miller Map Based on the Caputo h-Difference Operator: Linear Methods for Chaos Control and Synchronization Discrete Dynamics in Nature and Society |
| title | Fractional Grassi–Miller Map Based on the Caputo h-Difference Operator: Linear Methods for Chaos Control and Synchronization |
| title_full | Fractional Grassi–Miller Map Based on the Caputo h-Difference Operator: Linear Methods for Chaos Control and Synchronization |
| title_fullStr | Fractional Grassi–Miller Map Based on the Caputo h-Difference Operator: Linear Methods for Chaos Control and Synchronization |
| title_full_unstemmed | Fractional Grassi–Miller Map Based on the Caputo h-Difference Operator: Linear Methods for Chaos Control and Synchronization |
| title_short | Fractional Grassi–Miller Map Based on the Caputo h-Difference Operator: Linear Methods for Chaos Control and Synchronization |
| title_sort | fractional grassi miller map based on the caputo h difference operator linear methods for chaos control and synchronization |
| url | http://dx.doi.org/10.1155/2020/8825694 |
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