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