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

Abstract

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.