23 results on '"Ouannas, Adel"'
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2. HYPERCHAOTIC DYNAMICS OF A NEW FRACTIONAL DISCRETE-TIME SYSTEM.
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KHENNAOUI, AMINA-AICHA, OUANNAS, ADEL, MOMANI, SHAHER, DIBI, ZOHIR, GRASSI, GIUSEPPE, BALEANU, DUMITRU, and PHAM, VIET-THANH
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DISCRETE-time systems , *LYAPUNOV exponents , *BIFURCATION diagrams , *POINCARE maps (Mathematics) , *FRACTIONAL calculus , *ENTROPY - Abstract
In recent years, some efforts have been devoted to nonlinear dynamics of fractional discrete-time systems. A number of papers have so far discussed results related to the presence of chaos in fractional maps. However, less results have been published to date regarding the presence of hyperchaos in fractional discrete-time systems. This paper aims to bridge the gap by introducing a new three-dimensional fractional map that shows, for the first time, complex hyperchaotic behaviors. A detailed analysis of the map dynamics is conducted via computation of Lyapunov exponents, bifurcation diagrams, phase portraits, approximated entropy and C 0 complexity. Simulation results confirm the effectiveness of the approach illustrated herein. [ABSTRACT FROM AUTHOR]
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- 2021
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3. On the Dynamics and Control of Fractional Chaotic Maps with Sine Terms.
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Gasri, Ahlem, Ouannas, Adel, Khennaoui, Amina-Aicha, Bendoukha, Samir, and Pham, Viet-Thanh
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POINCARE maps (Mathematics) , *BIFURCATION diagrams , *LYAPUNOV exponents , *CHARTS, diagrams, etc. , *FRACTIONAL calculus - Abstract
This paper studies the dynamics of two fractional-order chaotic maps based on two standard chaotic maps with sine terms. The dynamic behavior of this map is analyzed using numerical tools such as phase plots, bifurcation diagrams, Lyapunov exponents and 0–1 test. With the change of fractional-order, it is shown that the proposed fractional maps exhibit a range of different dynamical behaviors including coexisting attractors. The existence of coexistence attractors is depicted by plotting bifurcation diagram for two symmetrical initial conditions. In addition, three control schemes are introduced. The first two controllers stabilize the states of the proposed maps and ensure their convergence to zero asymptotically whereas the last synchronizes a pair of non-identical fractional maps. Numerical results are used to verify the findings. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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4. Bifurcation and chaos in the fractional form of Hénon-Lozi type map.
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Ouannas, Adel, Khennaoui, Amina–Aicha, Wang, Xiong, Pham, Viet-Thanh, Boulaaras, Salah, and Momani, Shaher
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LYAPUNOV exponents , *BIFURCATION diagrams , *FRACTIONAL calculus - Abstract
In this paper, we are particularly interested in the fractional form of the Hénon-Lozi type map. Using discrete fractional calculus, we show that the general behavior of the proposed fractional order map depends on the fractional order. The dynamical properties of the new generalized map are investigated by applying numerical tools such as: phase portrait, bifurcation diagram, largest Lyapunov exponent, and 0-1 test. It shows that the fractional order Hénon-Lozi map exhibits a range of different dynamical behaviors including chaos and coexisting attractors. Furthermore, a one-dimensional control law is proposed to stabilize the states of the fractional order map. Numerical results are presented to illustrate the findings. [ABSTRACT FROM AUTHOR]
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- 2020
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5. On the Q–S Chaos Synchronization of Fractional-Order Discrete-Time Systems: General Method and Examples.
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Ouannas, Adel, Khennaoui, Amina-Aicha, Grassi, Giuseppe, and Bendoukha, Samir
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CHAOS theory , *FRACTIONAL calculus , *DISCRETE-time systems , *STABILITY theory , *SYNCHRONIZATION - Abstract
In this paper, we propose two control strategies for the Q–S synchronization of fractional-order discrete-time chaotic systems. Assuming that the dimension of the response system m is higher than that of the drive system n, the first control scheme achieves n-dimensional synchronization whereas the second deals with the m-dimensional case. The stability of the proposed schemes is established by means of the linearization method. Numerical results are presented to confirm the findings of the study. [ABSTRACT FROM AUTHOR]
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- 2018
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6. A simple fractional-order chaotic system without equilibrium and its synchronization.
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Pham, Viet-Thanh, Ouannas, Adel, Volos, Christos, and Kapitaniak, Tomasz
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FRACTIONAL calculus , *CHAOS theory , *ELECTRIC circuits , *SYNCHRONIZATION , *ATTRACTORS (Mathematics) - Abstract
There has been an increasing interest in discovering no-equilibrium chaotic systems recently. In this paper, a novel three dimensional fractional-order chaotic system, which has no equilibrium, is introduced. Dynamics of the system has been studied. It is interesting that the system can exhibit coexisting chaotic attractors for the order as low as 2.7. The adjustable feature of a variable is studied by introducing a single controlled constant. Circuit implementation of the system is proposed to show its feasibility. In addition, we have designed the controllers to investigate coexisting synchronization types of such a new fractional-order system. Numerical examples have verified the proposed synchronization schemes. [ABSTRACT FROM AUTHOR]
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- 2018
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7. On a function projective synchronization scheme for non-identical Fractional-order chaotic (hyperchaotic) systems with different dimensions and orders.
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Ouannas, Adel, Grassi, Giuseppe, Ziar, Toufik, and Odibat, Zaid
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CHAOS theory , *SYNCHRONIZATION , *FRACTIONAL calculus , *LORENZ equations , *SCALING laws (Statistical physics) - Abstract
Referring to fractional-order systems, this paper investigates the inverse full state hybrid function projective synchronization (IFSHFPS) of non-identical systems characterized by different dimensions and different orders . By taking a master system of dimension n and a slave system of dimension m , the method enables each master system state to be synchronized with a linear combination of slave system states, where the scaling factor of the linear combination can be any arbitrary differentiable function. The approach presents some useful features: i) it enables commensurate and incommensurate non-identical fractional-order systems with different dimension n < m or n > m to be synchronized; ii) it can be applied to a wide class of chaotic (hyperchaotic) fractional-order systems for any differentiable scaling function; iii) it is rigorous, being based on two theorems, one for the case n < m and the other for the case n > m . Two different numerical examples are reported, involving chaotic/hyperchaotic fractional-order Lorenz systems (three-dimensional and four-dimensional master/slave, respectively) and hyperchaotic/chaotic fractional-order Chen systems (four-dimensional and three-dimensional master/slave, respectively). The examples clearly highlight the capability of the conceived approach in effectively achieving synchronized dynamics for any differentiable scaling function. [ABSTRACT FROM AUTHOR]
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- 2017
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8. Fractional chaos synchronization schemes for different dimensional systems with non-identical fractional-orders via two scaling matrices.
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Ouannas, Adel, Al-sawalha, M. Mossa, and Ziar, Toufik
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FRACTIONAL calculus , *CHAOS theory , *MATRICES (Mathematics) , *NUMERICAL analysis , *LYAPUNOV functions , *COMPUTER simulation - Abstract
By using two scaling matrices, the synchronization problem of different dimensional fractional order chaotic systems in different dimensions is developed in this article. The controller is designed to assure that the synchronization of two different dimensional fractional order chaotic systems is achieved using the fractional-order Lyapunov direct method. Numerical examples and computer simulations are used to validate numerically the proposed synchronization schemes. [ABSTRACT FROM AUTHOR]
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- 2016
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9. On Fractional-Order Discrete-Time Reaction Diffusion Systems.
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Almatroud, Othman Abdullah, Hioual, Amel, Ouannas, Adel, and Grassi, Giuseppe
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DIFFERENCE operators , *FRACTIONAL calculus , *DISCRETE-time systems , *SYSTEM dynamics , *MALONIC acid - Abstract
Reaction–diffusion systems have a broad variety of applications, particularly in biology, and it is well known that fractional calculus has been successfully used with this type of system. However, analyzing these systems using discrete fractional calculus is novel and requires significant research in a diversity of disciplines. Thus, in this paper, we investigate the discrete-time fractional-order Lengyel–Epstein system as a model of the chlorite iodide malonic acid (CIMA) chemical reaction. With the help of the second order difference operator, we describe the fractional discrete model. Furthermore, using the linearization approach, we established acceptable requirements for the local asymptotic stability of the system's unique equilibrium. Moreover, we employ a Lyapunov functional to show that when the iodide feeding rate is moderate, the constant equilibrium solution is globally asymptotically stable. Finally, numerical models are presented to validate the theoretical conclusions and demonstrate the impact of discretization and fractional-order on system dynamics. The continuous version of the fractional-order Lengyel–Epstein reaction–diffusion system is compared to the discrete-time system under consideration. [ABSTRACT FROM AUTHOR]
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- 2023
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10. On Variable-Order Fractional Discrete Neural Networks: Existence, Uniqueness and Stability.
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Almatroud, Othman Abdullah, Hioual, Amel, Ouannas, Adel, Sawalha, Mohammed Mossa, Alshammari, Saleh, and Alshammari, Mohammad
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FRACTIONAL calculus , *COMPUTER simulation - Abstract
Given the recent advances regarding the studies of discrete fractional calculus, and the fact that the dynamics of discrete-time neural networks in fractional variable-order cases have not been sufficiently documented, herein, we consider a novel class of discrete-time fractional-order neural networks using discrete nabla operator of variable-order. An adequate criterion for the existence of the solution in addition to its uniqueness for such systems is provided with the use of Banach fixed point technique. Moreover, the uniform stability is investigated. We provide at the end two numerical simulations illustrating the relevance of the aforementioned results. [ABSTRACT FROM AUTHOR]
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- 2023
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11. Modified Three-Point Fractional Formulas with Richardson Extrapolation.
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Batiha, Iqbal M., Alshorm, Shameseddin, Ouannas, Adel, Momani, Shaher, Ababneh, Osama Y., and Albdareen, Meaad
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EXTRAPOLATION , *FRACTIONAL calculus , *VALUES (Ethics) - Abstract
In this paper, we introduce new three-point fractional formulas which represent three generalizations for the well-known classical three-point formulas; central, forward and backward formulas. This has enabled us to study the function's behavior according to different fractional-order values of α numerically. Accordingly, we then introduce a new methodology for Richardson extrapolation depending on the fractional central formula in order to obtain a high accuracy for the gained approximations. We compare the efficiency of the proposed methods by using tables and figures to show their reliability. [ABSTRACT FROM AUTHOR]
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- 2022
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12. Bifurcations, Hidden Chaos and Control in Fractional Maps.
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Ouannas, Adel, Almatroud, Othman Abdullah, Khennaoui, Amina Aicha, Alsawalha, Mohammad Mossa, Baleanu, Dumitru, Huynh, Van Van, and Pham, Viet-Thanh
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NONLINEAR dynamical systems , *POINCARE maps (Mathematics) , *BIFURCATION diagrams , *CHAOS theory , *FRACTIONAL calculus - Abstract
Recently, hidden attractors with stable equilibria have received considerable attention in chaos theory and nonlinear dynamical systems. Based on discrete fractional calculus, this paper proposes a simple two-dimensional and three-dimensional fractional maps. Both fractional maps are chaotic and have a unique equilibrium point. Results show that the dynamics of the proposed fractional maps are sensitive to both initial conditions and fractional order. There are coexisting attractors which have been displayed in terms of bifurcation diagrams, phase portraits and a 0-1 test. Furthermore, control schemes are introduced to stabilize the chaotic trajectories of the two novel systems. [ABSTRACT FROM AUTHOR]
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- 2020
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13. Chaos, control, and synchronization in some fractional-order difference equations.
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Khennaoui, Amina-Aicha, Ouannas, Adel, Bendoukha, Samir, Grassi, Giuseppe, Wang, Xiong, Pham, Viet-Thanh, and Alsaadi, Fawaz E.
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DIFFERENCE equations , *BIFURCATION diagrams , *SYNCHRONIZATION , *STABILITY theory , *DISCRETE systems , *FRACTIONAL calculus - Abstract
In this paper, we propose three fractional chaotic maps based on the well known 3D Stefanski, Rössler, and Wang maps. The dynamics of the proposed fractional maps are investigated experimentally by means of phase portraits, bifurcation diagrams, and Lyapunov exponents. In addition, three control laws are introduced for these fractional maps and the convergence of the controlled states towards zero is guaranteed by means of the stability theory of linear fractional discrete systems. Furthermore, a combined synchronization scheme is introduced whereby the fractional Rössler map is considered as a drive system with the response system being a combination of the remaining two maps. Numerical results are presented throughout the paper to illustrate the findings. [ABSTRACT FROM AUTHOR]
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- 2019
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14. Synchronization results for a class of fractional-order spatiotemporal partial differential systems based on fractional Lyapunov approach.
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Ouannas, Adel, Wang, Xiong, Pham, Viet-Thanh, Grassi, Giuseppe, and Huynh, Van Van
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SYNCHRONIZATION , *NEUMANN boundary conditions - Abstract
In this paper, the problem of synchronization of a class of spatiotemporal fractional-order partial differential systems is studied. Subject to homogeneous Neumann boundary conditions and using fractional Lyapunov approach, nonlinear and linear control schemes have been proposed to synchronize coupled general fractional reaction–diffusion systems. As a numerical application, we investigate complete synchronization behaviors of coupled fractional Lengyel–Epstein systems. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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15. The fractional form of a new three-dimensional generalized Hénon map.
- Author
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Jouini, Lotfi, Ouannas, Adel, Khennaoui, Amina-Aicha, Wang, Xiong, Grassi, Giuseppe, and Pham, Viet-Thanh
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LYAPUNOV exponents , *BIFURCATION diagrams , *FRACTIONAL calculus - Abstract
In this paper, we propose a fractional form of a new three-dimensional generalized Hénon map and study the existence of chaos and its control. Using bifurcation diagrams, phase portraits and Lyapunov exponents, we show that the general behavior of the proposed fractional map depends on the fractional order. We also present two control schemes for the proposed map, one that adaptively stabilizes the fractional map, and another to achieve the synchronization of the proposed fractional map. [ABSTRACT FROM AUTHOR]
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- 2019
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16. Fractional Form of a Chaotic Map without Fixed Points: Chaos, Entropy and Control.
- Author
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Ouannas, Adel, Wang, Xiong, Khennaoui, Amina-Aicha, Bendoukha, Samir, Pham, Viet-Thanh, and Alsaadi, Fawaz E.
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ENTROPY , *CHAOS theory , *FIXED point theory , *BIFURCATION diagrams , *FRACTIONAL calculus - Abstract
In this paper, we investigate the dynamics of a fractional order chaotic map corresponding to a recently developed standard map that exhibits a chaotic behavior with no fixed point. This is the first study to explore a fractional chaotic map without a fixed point. In our investigation, we use phase plots and bifurcation diagrams to examine the dynamics of the fractional map and assess the effect of varying the fractional order. We also use the approximate entropy measure to quantify the level of chaos in the fractional map. In addition, we propose a one-dimensional stabilization controller and establish its asymptotic convergence by means of the linearization method. [ABSTRACT FROM AUTHOR]
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- 2018
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17. The Co-existence of Different Synchronization Types in Fractional-order Discrete-time Chaotic Systems with Non–identical Dimensions and Orders.
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Bendoukha, Samir, Ouannas, Adel, Wang, Xiong, Khennaoui, Amina-Aicha, Pham, Viet-Thanh, Grassi, Giuseppe, and Huynh, Van Van
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SYNCHRONIZATION , *FRACTIONAL calculus , *DISCRETE-time systems , *NONLINEAR control theory , *CHAOS theory - Abstract
This paper is concerned with the co-existence of different synchronization types for fractional-order discrete-time chaotic systems with different dimensions. In particular, we show that through appropriate nonlinear control, projective synchronization (PS), full state hybrid projective synchronization (FSHPS), and generalized synchronization (GS) can be achieved simultaneously. A second nonlinear control scheme is developed whereby inverse full state hybrid projective synchronization (IFSHPS) and inverse generalized synchronization (IGS) are shown to co-exist. Numerical examples are presented to confirm the findings. [ABSTRACT FROM AUTHOR]
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- 2018
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18. Generalized and inverse generalized synchronization of fractional-order discrete-time chaotic systems with non-identical dimensions.
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Khennaoui, Amina-Aicha, Ouannas, Adel, Bendoukha, Samir, Grassi, Giuseppe, Wang, Xiong, and Pham, Viet-Thanh
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DISCRETE-time systems , *GENERALIZABILITY theory , *CHAOS theory , *FRACTIONAL calculus , *DIMENSIONS - Abstract
In this paper, we introduce two approaches to the generalized synchronized synchronization and the inverse generalized synchronization of fractional discrete-time chaotic systems with non-identical dimensions. The convergence of the proposed approaches is established by means of recently developed stability theory. Numerical results are presented based on well-known maps in the literature. Two examples are considered: a 3D generalized synchronization and a 2D inverse generalized synchronization. [ABSTRACT FROM AUTHOR]
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- 2018
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19. On Chaos and Complexity Analysis for a New Sine-Based Memristor Map with Commensurate and Incommensurate Fractional Orders.
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Hamadneh, Tareq, Abbes, Abderrahmane, Al-Tarawneh, Hassan, Gharib, Gharib Mousa, Salameh, Wael Mahmoud Mohammad, Al Soudi, Maha S., and Ouannas, Adel
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BIFURCATION diagrams , *NONLINEAR analysis , *LYAPUNOV exponents , *FRACTIONAL calculus - Abstract
In this study, we expand a 2D sine map via adding the discrete memristor to introduce a new 3D fractional-order sine-based memristor map. Under commensurate and incommensurate orders, we conduct an extensive exploration and analysis of its nonlinear dynamic behaviors, employing diverse numerical techniques, such as analyzing Lyapunov exponents, visualizing phase portraits, and plotting bifurcation diagrams. The results emphasize the sine-based memristor map's sensitivity to fractional-order parameters, resulting in the emergence of distinct and diverse dynamic patterns. In addition, we employ the sample entropy ( S a m p E n ) method and C 0 complexity to quantitatively measure complexity, and we also utilize the 0–1 test to validate the presence of chaos in the proposed fractional-order sine-based memristor map. Finally, MATLAB simulations are be executed to confirm the results provided. [ABSTRACT FROM AUTHOR]
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- 2023
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20. On Ikeda-Based Memristor Map with Commensurate and Incommensurate Fractional Orders: Bifurcation, Chaos, and Entropy.
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Alsayyed, Omar, Abbes, Abderrahmane, Gharib, Gharib Mousa, Abualhomos, Mayada, Al-Tarawneh, Hassan, Al Soudi, Maha S., Abu-Alkishik, Nabeela, Al-Husban, Abdallah, and Ouannas, Adel
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LYAPUNOV exponents , *POLITICAL stability , *BIFURCATION diagrams , *DYNAMIC stability , *TOPOLOGICAL entropy , *FRACTIONAL calculus - Abstract
This paper introduces a novel fractional Ikeda-based memristor map and investigates its non-linear dynamics under commensurate and incommensurate orders using various numerical techniques, including Lyapunov exponent analysis, phase portraits, and bifurcation diagrams. The results reveal diverse and complex system behaviors arising from the interplay of different fractional orders in the proposed map. Furthermore, the study employs the sample entropy test to quantify complexity and validate the presence of chaos. Non-linear controllers are also presented to stabilize and synchronize the model. The research emphasizes the system's sensitivity to the fractional order parameters, leading to distinct dynamic patterns and stability regimes. The memristor-based chaotic map exhibits rich and intricate behavior, making it an interesting and important area of research. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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21. Bifurcation, Hidden Chaos, Entropy and Control in Hénon-Based Fractional Memristor Map with Commensurate and Incommensurate Orders.
- Author
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Abualhomos, Mayada, Abbes, Abderrahmane, Gharib, Gharib Mousa, Shihadeh, Abdallah, Al Soudi, Maha S., Alsaraireh, Ahmed Atallah, and Ouannas, Adel
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LYAPUNOV exponents , *BIFURCATION diagrams , *TOPOLOGICAL entropy , *MAPS , *FRACTIONAL calculus - Abstract
In this paper, we present an innovative 3D fractional Hénon-based memristor map and conduct an extensive exploration and analysis of its dynamic behaviors under commensurate and incommensurate orders. The study employs diverse numerical techniques, such as visualizing phase portraits, analyzing Lyapunov exponents, plotting bifurcation diagrams, and applying the sample entropy test to assess the complexity and validate the chaotic characteristics. However, since the proposed fractional map has no fixed points, the outcomes reveal that the map can exhibit a wide range of hidden dynamical behaviors. This phenomenon significantly augments the complexity of the fractal structure inherent to the chaotic attractors. Moreover, we introduce nonlinear controllers designed for stabilizing and synchronizing the proposed fractional Hénon-based memristor map. The research emphasizes the system's sensitivity to fractional-order parameters, resulting in the emergence of distinct dynamic patterns. The memristor-based chaotic map exhibits rich and intricate behavior, making it a captivating and significant area of investigation. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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22. Finite Time Stability Results for Neural Networks Described by Variable-Order Fractional Difference Equations.
- Author
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Hamadneh, Tareq, Hioual, Amel, Alsayyed, Omar, Al-Khassawneh, Yazan Alaya, Al-Husban, Abdallah, and Ouannas, Adel
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DIFFERENCE equations , *GRONWALL inequalities , *FRACTIONAL calculus , *ENGINEERING models , *SCIENTIFIC community , *PULSATILE flow - Abstract
Variable-order fractional discrete calculus is a new and unexplored part of calculus that provides extraordinary capabilities for simulating multidisciplinary processes. Recognizing this incredible potential, the scientific community has been researching variable-order fractional discrete calculus applications to the modeling of engineering and physical systems. This research makes a contribution to the topic by describing and establishing the first generalized discrete fractional variable order Gronwall inequality that we employ to examine the finite time stability of nonlinear Nabla fractional variable-order discrete neural networks. This is followed by a specific version of a generalized variable-order fractional discrete Gronwall inequality described using discrete Mittag–Leffler functions. A specific version of a generalized variable-order fractional discrete Gronwall inequality represented using discrete Mittag–Leffler functions is shown. As an application, utilizing the contracting mapping principle and inequality approaches, sufficient conditions are developed to assure the existence, uniqueness, and finite-time stability of the equilibrium point of the suggested neural networks. Numerical examples, as well as simulations, are provided to show how the key findings can be applied. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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23. Local Stability, Global Stability, and Simulations in a Fractional Discrete Glycolysis Reaction–Diffusion Model.
- Author
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Hamadneh, Tareq, Hioual, Amel, Alsayyed, Omar, AL-Khassawneh, Yazan Alaya, Al-Husban, Abdallah, and Ouannas, Adel
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FINITE differences , *PHENOMENOLOGICAL biology , *LYAPUNOV functions , *FRACTIONAL calculus , *DISCRETE systems , *GLYCOLYSIS , *DISCRETE-time systems - Abstract
In the last few years, reaction–diffusion models associated with discrete fractional calculus have risen in prominence in scientific fields, not just due to the requirement for numerical simulation but also due to the described biological phenomena. This work investigates a discrete equivalent of the fractional reaction–diffusion glycolysis model. The discrete fractional calculus tool is introduced to the discrete modeling of diffusion problems in the Caputo-like delta sense, and a fractional discretization diffusion model is described. The local stability of the equilibrium points in the proposed discrete system is examined. We additionally investigate the global stability of the equilibrium point by developing a Lyapunov function. Furthermore, this study indicates that the L1 finite difference scheme and the second-order central difference scheme can successfully preserve the characteristics of the associated continuous system. Finally, an equivalent summation representing the model's numerical formula is shown. The diffusion concentration is further investigated for different fractional orders, and examples with simulations are presented to corroborate the theoretical findings. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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