Fractional-Order Hybrid Synchronization for Multiple Hyperchaotic Systems

Lassoued, Abir; Boubaker, Olfa

doi:10.1016/b978-0-12-815838-8.00017-0

Cited by 3 publications

(4 citation statements)

References 14 publications

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“…The Fractional-Order MatLab (Simulink) method, is used for solving the dynamics (3) and ( 4) with nonlinear control laws ( 14), (17), and (22) for time-delay synchronization, and nonlinear control laws (35), (40), and (45) for time-delay anti-synchronization. For chaotic behavior of the fractional-order Chen system (3) and Lorenz system (4), their controllers with the fractional-order PID control law, together, show the synchronization and anti-synchronization behavior, and the modeling errors tend to zero, as can be seen in Figures 1 and 2 with 𝛼 = 0.9, and in the Figures 3 and 4 the variable-order fractional with 𝛼 = 0.9, 𝛼 = 0.8, and 𝛼 = 0.5.…”

Section: Discussionmentioning

confidence: 99%

“…In summary we have: with which, the time-delay system (4) is synchronized with system (3), using the control laws obtained previously ( 12), (17), and ( 22) and the adaptation laws (estimation), given by Equations ( 25)-( 27). Therefore, we have the following theorem:…”

Section: Time-delay Adaptive Synchronization Of Chaotic Systems Of Fr...mentioning

confidence: 99%

“…The time-delay synchronization and anti-synchronization between the Chen and Lorenz systems are obtained by means of the control laws ( 12), (17), and (22), and the analysis of the convergence of the approximation errors of these systems is guaranteed via the Lyapunov stability analysis for systems of fractional order and the fractional order PIDtype control law. The fractional-order derivative in this paper is using α = 0.9 and α = 0.9, α = 0.8, α = 0.5, and the time delay 𝜏 = 5 seg, and the initial conditions for simulation are 𝑥(0) = [−10, 0, 37] and 𝑦(0) = [10, 0, 10] for synchronization and anti-synchronization and the graphs of the Lorenz values, which are the laws of adaptation.…”

Section: Simulationsmentioning

confidence: 99%

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Time-Delay Fractional Variable Order Adaptive Synchronization and Anti-Synchronization between Chen and Lorenz Chaotic Systems Using Fractional Order PID Control

et al. 2022

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In this research work, time-delay adaptive synchronization and adaptive anti-synchronization of chaotic fractional order systems are analyzed via the Caputo fractional derivative, and the prob-lem of synchronization and anti-synchronization of chaotic systems of variable fractional order is solved by using the fractional order PID control law, the adaptive laws of variable-order frac-tional calculus, and a control law deduced from Lyapunov’s theory extended to systems of time-delay variable-order fractional calculus. In this research work, two important problems are solved in the control area: The first problem is described in which deals with syn-chro-nization of chaotic systems of adaptive fractional order with time delay, this problem is solved by using the fractional order PID control law and adaptative laws. The second problem is de-scribed in which deals with anti-synchronization of chaotic systems of adaptive frac-tional order with time delay, and this problem is solved by using the fractional order PID con-trol law and adaptative laws.

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Section: Discussionmentioning

confidence: 99%

Section: Time-delay Adaptive Synchronization Of Chaotic Systems Of Fr...mentioning

confidence: 99%

Section: Simulationsmentioning

confidence: 99%

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Time-Delay Fractional Variable Order Adaptive Synchronization and Anti-Synchronization between Chen and Lorenz Chaotic Systems Using Fractional Order PID Control

et al. 2022

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“…The advantage of this definition is that the function under study does not have to be continuous at the origin. It does not have to be differentiable either [ 31 ].…”

Section: Fractional Order Derivativementioning

confidence: 99%

Fractional Derivatives Application to Image Fusion Problems

Motłoch

Sarwas

Dzieliński

2022

Sensors

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In this paper, an analysis of the method that uses a fractional order calculus to multispectral images fusion is presented. We analyze some correct basic definitions of the fractional order derivatives that are used in the image processing context. Several methods of determining fractional derivatives of digital images are tested, and the influence of fractional order change on the quality of fusion is presented. Results achieved are compared with the results obtained for methods where the integer order derivatives were used.

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Secure Communication: Using Double Compound-Combination Hybrid Synchronization

Trikha

Jahanzaib

2020

Proceedings of International Conference on Artificial Intelligence and Applications

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Fractional-Order Hybrid Synchronization for Multiple Hyperchaotic Systems

Cited by 3 publications

References 14 publications

Time-Delay Fractional Variable Order Adaptive Synchronization and Anti-Synchronization between Chen and Lorenz Chaotic Systems Using Fractional Order PID Control

Time-Delay Fractional Variable Order Adaptive Synchronization and Anti-Synchronization between Chen and Lorenz Chaotic Systems Using Fractional Order PID Control

Fractional Derivatives Application to Image Fusion Problems

Secure Communication: Using Double Compound-Combination Hybrid Synchronization

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