On fractional and distributed order hyperchaotic systems with line and parabola of equilibrium points and their synchronization

Mahmoud, Gamal M.; Abed‐Elhameed, Tarek M.; Khalaf, Hesham

doi:10.1088/1402-4896/ac0f3c

Cited by 10 publications

(8 citation statements)

References 50 publications

(83 reference statements)

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“…Synchronization among fractional-order Lü model and a model of integer-order was presented [23]. Mahmoud et al [24,25] investigated the generalization of combinationcombination synchronization among two fractional-order hyperchaotic models and two distributed-order hyperchaotic models. On the other hand, for the coupled chaotic models there exist a little papers for chaos desynchronization.…”

Section: Introductionmentioning

confidence: 99%

Synchronization and desynchronization of chaotic models with integer, fractional and distributed-orders and a color image encryption application

et al. 2023

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For the first time, as we know, the generalization of combination synchronization (GCS) of chaotic dynamical models with integer, fractional and distributed-orders is studied in this paper. In the literature, this type of synchronization is considered as a generalization of numerous other kinds. We state the definition of GCS and it’s scheme using tracking control technique among two drive integer and fractional-order models and one response distributed-order model. A theorem is established and proven to give us the analyticalformula for the control functions in order to achieve GCS. Numerical calculations are utilized to support these analytic results. We give an example to check the validity of the control functions to achieve GCS. Using the modified Predictor-Corrector method, we obtained numerical results for our models that are in good agreement with the analytical ones. In this work, also, we introduce both of the fractional-order hyperchaotic strongly coupled (FOHSC) Lorenz model and distributed-order hyperchaotic strongly coupled (DOHSC) Lorenz model. Since there are few articles on chaos desynchronization, we aim to study the chaos desynchronization of FOHSC and DOHSC Lorenz models. The encryption and decryption of color image are presented based on GCS between two drive integer and fractional-order models, respectively and one response distributed-order model. Information entropy, correlation analysis between adjacent pixels and histograms are determined together with the experimental results of color image encryption.

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Section: Introductionmentioning

confidence: 99%

Synchronization and desynchronization of chaotic models with integer, fractional and distributed-orders and a color image encryption application

et al. 2023

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“…Fractional-order differential equations have several applications in various sciences, like physics, biology, and engineering [2][3][4][5]. Many models exist with chaotic and hyperchaotic behaviors in fractional-order models, such as Lorenz model [6], Lü model [7], van der Pol-Duffing model [8], Chen model [9], Burke-Shaw model [10], and the modified Lü, Chen, and Lorenz models [11].…”

Section: Introductionmentioning

confidence: 99%

On the fractional‐order simplified Lorenz models: Dynamics, synchronization, and medical image encryption

Mahmoud

Khalaf

Darwish

et al. 2023

Math Methods in App Sciences

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This article discusses, for the first time as we know, the basic dynamics of commensurate and noncommensurate fractional‐order simplified Lorenz models, such as invariance, dissipation, stationary points, and the coexistence of chaotic attractors. These models have chaotic attractors and circles of stationary points. Our suggested models are derived from the Lorenz model, which appears in physics, engineering, and medicine (e.g., secure communications). Based on the tracking control method, we investigate a scheme for studying dual compound combination synchronization (DCCS) among 10 fractional‐order chaotic models. This kind of synchronization is a generalization of many other types in the literature. In order to achieve this type of synchronization, a theorem is established and proven to give us the analytical formula for the control functions. These analytical results are supported by numerical calculations. The encryption and decryption of medical image are presented based on DCCS of 10 fractional‐order chaotic models. Information entropy, correlation analysis between adjacent pixels, and histograms are computed together with the experimental results of medical image encryption.

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“…e tracking control strategies for continuous chaotic systems, for example, are addressed in references [10,19]. Mahmoud et al [10] presented the function projective combination synchronization for chaotic fractional-order systems using tracking control.…”

Section: Introductionmentioning

confidence: 99%

“…Mahmoud et al [10] presented the function projective combination synchronization for chaotic fractional-order systems using tracking control. While the authors in Ref [19] investigated the combination-combination synchronization between two fractional-order systems and two distributed-order systems by tracking a control scheme. e aim of this paper is to introduce the chaotic fractional-order Sprott Q system and its dynamics.…”

Section: Introductionmentioning

confidence: 99%

Tracking Control Method for Double Compound-Combination Synchronization of Fractional Chaotic Systems and Its Application in Secure Communication

Themairi

Abed‐Elhameed

Farghaly

2022

Mathematical Problems in Engineering

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This paper introduces the chaotic fractional-order Sprott Q system and its dynamics. The double compound combination of eight fractional-order chaotic synchronizations was investigated. This kind of synchronization is considered a generalization of many types of synchronization given in the literature. The analytical formula of the control functions is developed and proven using the tracking control method. As we know the fractional derivatives of two multiple functions are very difficult to calculate, and the tracking control method is more suitable for this kind of synchronization. This technique’s communication is more secure and reliable because there are more drive and response systems. To achieve the proposed synchronization, four driving and four response identical chaotic systems are used as an example. This scheme may be used in many applications such as secure communications and safe information. Using the proposed double compound-combination synchronization is an example given to encrypt a message. The analytical results were confirmed by numerical simulation, and we found good agreement.

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On fractional and distributed order hyperchaotic systems with line and parabola of equilibrium points and their synchronization

Cited by 10 publications

References 50 publications

Synchronization and desynchronization of chaotic models with integer, fractional and distributed-orders and a color image encryption application

Synchronization and desynchronization of chaotic models with integer, fractional and distributed-orders and a color image encryption application

On the fractional‐order simplified Lorenz models: Dynamics, synchronization, and medical image encryption

Tracking Control Method for Double Compound-Combination Synchronization of Fractional Chaotic Systems and Its Application in Secure Communication

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