A variable-order fractional memristor neural network: Secure image encryption and synchronization via a smooth and robust control approach

In this research, we introduce and investigate a variable-order fractional memristor neural network, focusing on its engineering applications in synchronization and image encryption. This study stands out as a pioneering effort in proposing such an architecture for image encryption purposes. Distinct from conventional fractional-order systems, our model incorporates a time-varying fractional derivative, leading to more complex behaviors. Through numerical simulations, we vividly demonstrate the chaotic dynamics of the system. Our results further reveal the system's outstanding performance in image encryption applications. To augment the system's efficiency, we introduce a robust control strategy that guarantees smooth stabilization and synchronization of the variable-order fractional system. Considering the unique variable-order fractional nature of the system, we provide theoretical validations and empirical evidence supporting its stability and convergence properties. Additionally, we present synchronization outcomes between pairs of such neural networks employing our robust control approach. Our numerical analyses firmly substantiate the superiority of our control strategy, particularly highlighting its precision, robustness, and ability to maintain chattering-free performance under external disturbances.