Adjusting Dynamics of Hopfield Neural Network via Time-variant Stimulus

As a paradigmatic model for nonlinear dynamics studies, the Hopfield Neural Network (HNN) demonstrates a high susceptibility to external disturbances owing to its intricate structure. This paper delves into the challenge of modulating HNN dynamics through time-variant stimuli. The effects of adjustments using two distinct types of time-variant stimuli, namely the Weight Matrix Stimulus (WMS) and the State Variable Stimulus (SVS), along with a Constant Stimulus (CS) are reported. The findings reveal that deploying four WMSs enables the HNN to generate either a four-scroll or a coexisting two-scroll attractor. When combined with one SVS, four WMSs can lead to the formation of an eight-scroll or four-scroll attractor, while the integration of four WMSs and multiple SVSs can induce grid-multi-scroll attractors. Moreover, the introduction of a CS and an SVS can significantly disrupt the dynamic behavior of the HNN. Consequently, suitable adjustment methods are crucial for enhancing the network's dynamics, whereas inappropriate applications can lead to the loss of its chaotic characteristics. To empirically validate these enhancement effects, the study employs an FPGA hardware platform. Subsequently, an image encryption scheme is designed to demonstrate the practical application benefits of the dynamically adjusted HNN in secure multimedia communication. This exploration into the dynamic modulation of HNN via time-variant stimuli offers insightful contributions to the advancement of secure communication technologies.