Fractional Grassi–Miller Map Based on the Caputo h-Difference Operator: Linear Methods for Chaos Control and Synchronization
Joint Authors
Grassi, Giuseppe
Pham, Viet-Thanh
Baleanu, Dumitru
Ouannas, Adel
Talbi, Ibtissem
Khennaoui, Amina-Aicha
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-11-26
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Talbi, Ibtissem& Ouannas, Adel& Grassi, Giuseppe& Khennaoui, Amina-Aicha& Pham, Viet-Thanh& Baleanu, Dumitru. 2020. Fractional Grassi–Miller Map Based on the Caputo h-Difference Operator: Linear Methods for Chaos Control and Synchronization. Discrete Dynamics in Nature and Society،Vol. 2020, no. 2020, pp.1-10.
https://search.emarefa.net/detail/BIM-1153540
Modern Language Association (MLA)
Talbi, Ibtissem…[et al.]. Fractional Grassi–Miller Map Based on the Caputo h-Difference Operator: Linear Methods for Chaos Control and Synchronization. Discrete Dynamics in Nature and Society No. 2020 (2020), pp.1-10.
https://search.emarefa.net/detail/BIM-1153540
American Medical Association (AMA)
Talbi, Ibtissem& Ouannas, Adel& Grassi, Giuseppe& Khennaoui, Amina-Aicha& Pham, Viet-Thanh& Baleanu, Dumitru. Fractional Grassi–Miller Map Based on the Caputo h-Difference Operator: Linear Methods for Chaos Control and Synchronization. Discrete Dynamics in Nature and Society. 2020. Vol. 2020, no. 2020, pp.1-10.
https://search.emarefa.net/detail/BIM-1153540
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1153540