Bursting Firings in Memristive Hopfield Neural Network with Image Encryption and Hardware Implementation

By integrating memristors into a Hopfield neural network (HNN), a diverse range of dynamical behavior can be generated, which has significant implications for modeling and biomimetic applications of artificial neurons. However, research on the firing dynamics of HNNs remains relatively limited. In response, a memristive tri-neurons Hopfield neural network (MTN-HNN) was constructed, with the synapse of the second neuron replaced by the proposed memristor. A theoretical and experimental investigation of the dynamics of this neural network was conducted using general analytical tools, such as phase diagrams, Lyapunov exponents, bifurcation diagrams, and others. Experimental results indicate that the dynamics of the MTN-HNN is influenced by the internal parameters of the memristor, enabling the network to extend attractors in up to two directions and thereby form grid multi-scrolls. Notably, the MTN-HNN exhibits various firing modes, including periodic and chaotic bursting. Finally, an encryption scheme was proposed to demonstrate the potential of the MTN-HNN, and both the custom digital circuits and the encryption scheme were successfully implemented on a Field-Programmable Gate Array (FPGA).