Different orders jerk models: Dynamics, synchronization and their application in image encryption

This work introduced three different versions of a complex model called the chaotic hidden attractor jerk model. These versions were categorized as commensurate, non-commensurate, and distributed-order models. They can be applied in various practical fields like physics and image encryption. We explored the characteristics of these models such as fixed points, symmetry, and dissipation. These models exhibit chaotic behaviors, as evidenced by the Lyapunov exponent (LLE) and bifurcation diagram. We introduced a novel combination synchronization (CS) between these models using a tracking control method. We established a theorem for achieving synchronization among these different models. We presented numerical computations to validate the analytical results. Our research primarily focused on the encryption and decryption processes of grayscale images by the proposed synchronization method. We evaluated the efficacy of image encryption and decryption through various metrics like information entropy and histograms to ensure the accuracy and security of the process.