Dynamical Behaviour and Applications of Master-slave Fractional-order Non-volatile Memristor Chaotic Hopfield Neural Network

In this work, a discrete fractional-order memristor is proposed and proven to be non-volatile, which can be used to model synaptic connections between neurons. Based on the proposed memristor, we put forward a novel fractional order non-volatile memristor chaotic Hopfield neural network, utilizing a time-scale-based difference method for decoupling. The dynamical behaviours of the suggested fractional-order system are analyzed through phase diagram, Lyapunov exponent, divergence, stability analysis of equilibrium point and bifurcation diagram. A master-slave system is constructed based on the proposed system, thereby achieving synchronization and a novel image encryption approach is proposed, grounded in the master-slave hyperchaotic system obtained. The experimental findings indicate that the encrypted image exhibits an approximately uniform pixel distribution and adjacent pixel correlations close to zero, making it robust to statistical analysis attacks. Furthermore, the algorithm demonstrates resilience to differential attack, information entropy analysis and chosen plaintext attack. As a consequence of the parameter sensitivity of the proposed hyperchaotic system, the proposed encryption scheme features a considerable key space.