On Dynamics of a Fractional-Order Discrete System with Only One Nonlinear Term and without Fixed Points
Dynamical systems described by fractional-order difference equations have only been recently introduced inthe literature. Referring to chaotic phenomena, the type of the so-called “self-excited attractors” has been so far highlighted among different types of attractors by several recently presented...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Electronics |
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| Online Access: | https://www.mdpi.com/2079-9292/9/12/2179 |
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| author | Amina-Aicha Khennaoui Adel Ouannas Shaher Momani Iqbal M. Batiha Zohir Dibi Giuseppe Grassi |
| author_facet | Amina-Aicha Khennaoui Adel Ouannas Shaher Momani Iqbal M. Batiha Zohir Dibi Giuseppe Grassi |
| author_sort | Amina-Aicha Khennaoui |
| collection | DOAJ |
| description | Dynamical systems described by fractional-order difference equations have only been recently introduced inthe literature. Referring to chaotic phenomena, the type of the so-called “self-excited attractors” has been so far highlighted among different types of attractors by several recently presented fractional-order discrete systems. Quite the opposite, the type of the so-called “hidden attractors”, which can be characteristically revealed through exploring the same aforementioned systems, is almost unexplored in the literature. In view of those considerations, the present work proposes a novel 3D chaotic discrete system able to generate hidden attractors for some fractional-order values formulated for difference equations. The map, which is characterized by the absence of fixed points, contains only one nonlinear term in its dynamic equations. An appearance of hidden attractors in their chaotic modes is confirmed through performing some computations related to the 0–1 test, largest Lyapunov exponent, approximate entropy, and the bifurcation diagrams. Finally, a new robust control law of one-dimension is conceived for stabilizing the newly established 3D fractional-order discrete system. |
| first_indexed | 2024-03-10T13:58:10Z |
| format | Article |
| id | doaj.art-70494146f5de4648a84bd753cc1a4236 |
| institution | Directory Open Access Journal |
| issn | 2079-9292 |
| language | English |
| last_indexed | 2024-03-10T13:58:10Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Electronics |
| spelling | doaj.art-70494146f5de4648a84bd753cc1a42362023-11-21T01:27:27ZengMDPI AGElectronics2079-92922020-12-01912217910.3390/electronics9122179On Dynamics of a Fractional-Order Discrete System with Only One Nonlinear Term and without Fixed PointsAmina-Aicha Khennaoui0Adel Ouannas1Shaher Momani2Iqbal M. Batiha3Zohir Dibi4Giuseppe Grassi5Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, AlgeriaLaboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, AlgeriaNonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, UAENonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, UAEDepartment of Electronics, University of Batna 2, Batna 05000, AlgeriaDipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, ItalyDynamical systems described by fractional-order difference equations have only been recently introduced inthe literature. Referring to chaotic phenomena, the type of the so-called “self-excited attractors” has been so far highlighted among different types of attractors by several recently presented fractional-order discrete systems. Quite the opposite, the type of the so-called “hidden attractors”, which can be characteristically revealed through exploring the same aforementioned systems, is almost unexplored in the literature. In view of those considerations, the present work proposes a novel 3D chaotic discrete system able to generate hidden attractors for some fractional-order values formulated for difference equations. The map, which is characterized by the absence of fixed points, contains only one nonlinear term in its dynamic equations. An appearance of hidden attractors in their chaotic modes is confirmed through performing some computations related to the 0–1 test, largest Lyapunov exponent, approximate entropy, and the bifurcation diagrams. Finally, a new robust control law of one-dimension is conceived for stabilizing the newly established 3D fractional-order discrete system.https://www.mdpi.com/2079-9292/9/12/2179chaosdiscrete fractional calculuscoexisting attractors0–1 testapproximate entropycontrol law |
| spellingShingle | Amina-Aicha Khennaoui Adel Ouannas Shaher Momani Iqbal M. Batiha Zohir Dibi Giuseppe Grassi On Dynamics of a Fractional-Order Discrete System with Only One Nonlinear Term and without Fixed Points Electronics chaos discrete fractional calculus coexisting attractors 0–1 test approximate entropy control law |
| title | On Dynamics of a Fractional-Order Discrete System with Only One Nonlinear Term and without Fixed Points |
| title_full | On Dynamics of a Fractional-Order Discrete System with Only One Nonlinear Term and without Fixed Points |
| title_fullStr | On Dynamics of a Fractional-Order Discrete System with Only One Nonlinear Term and without Fixed Points |
| title_full_unstemmed | On Dynamics of a Fractional-Order Discrete System with Only One Nonlinear Term and without Fixed Points |
| title_short | On Dynamics of a Fractional-Order Discrete System with Only One Nonlinear Term and without Fixed Points |
| title_sort | on dynamics of a fractional order discrete system with only one nonlinear term and without fixed points |
| topic | chaos discrete fractional calculus coexisting attractors 0–1 test approximate entropy control law |
| url | https://www.mdpi.com/2079-9292/9/12/2179 |
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