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This article proposes an adaptive synchronization (AS) algorithm to synchronize a general class of fractional-order complex-valued systems with completely unknown parameters, which may appear in physical and engineering problems. The analytical and theoretical concepts of the algorithm rely on the mathematical framework of the Mittag-Leffler global stability of fractional-order systems. A specific control system is established analytically based on the fractional-order adaptive laws of parameters, and the corresponding numerical results are executed to verify the accuracy of the AS algorithm. The proposed synchronization method is evaluated using the fractional-order complex Rabinovich system as an attractive example. The electronic circuits of the new system with different fractional orders are designed. By utilizing the Multisim electronic workbench software, various chaotic/hyperchaotic behaviors have been observed, and a good agreement is found between the numerical results and experimental simulation. In addition, the approximation of the transfer function for different fractional-order are presented. And the corresponding resistor and capacitor values in the chain ship model (CSM) are estimated, which can be utilized in designing electronic circuits for other fractional-order systems. Furthermore, two strategies for encrypting color images are proposed using the AS algorithm and fractional-order adaptive laws of parameters. In the first strategy, the color image is treated as a single package and divided into two vectors. The first vector is embedded into transmitter parameters, while the second vector is injected into the transmitter state signals. In the second strategy, the primary RGB channel components of the original color image are extracted and separated into two vectors, and the same process is followed as in the first strategy. These strategies complicate the decryption task for intruders. Different scales of white Gaussian noise are added to color images to examine the robustness of the proposed color images encryption strategies

: This paper introduces the complex Rayleigh–van-der- Pol–Duffing oscillators (RVDOs), which are hyperchaotic and can be autonomous or nonautonomous. The fundamental dynamics of the autonomous and nonautonomous complex RVDOs, including dissipation, symmetry, fixed points, and stability, are studied. These oscillators are found in various necessary fields of physics and engineering. The paper proposes a scheme to achieve phase synchronization (PS) and antiphase synchronization (APS) for different dimensional models. These kinds of synchronization are considered a generalization of several other types of synchronization. We use the active control method based on Lyapunov’s stability theory for this scheme. By analytically determining the control functions, the scheme achieved PS and APS. Our scheme is applied to study the PS of hyperchaotic behaviors for two distinct hyperchaotic nonautonomous and autonomous complex RVDOs. Additionally, the scheme is employed to achieve the APS of a chaotic real nonautonomous RVDO and a hyperchaotic complex autonomous RVDO, including those with different dimensions. Our work presents numerical results that plot the amplitudes and phases of these hyperchaotic behaviors, demonstrating the achievement of the PS and APS. The encryption and decryption of grayscale images are researched based on APS. The experimental results of image encryption and decryption are computed with information entropy, visual analysis, and histograms.