Discrete Memristive Hopfield Neural Network and Application in Memristor-State-Based Encryption

Memristors can serve as variable synaptic weights between neurons for adaptive neural network regulation. Inspired by this, a discrete memristive Hopfield neural network (DM-HNN) is constructed utilizing an adaptive memristor weight instead of a fixed resistor weight. It has a line fixed point set with stability strongly related to the memristor initial state. On this basis, chaotic/hyperchaotic attractors with bifurcation dynamics are explored. Further, the memristor initial-boosting mechanism is examined and the memristor initial-boosted homogeneous attractors are elucidated. The results present that DM-HNN can exhibit chaotic/hyperchaotic attractors with intricate structures and memristor initial-boosted homogeneous attractors. Notably, the coexisting homogeneous sequences with excellent performance indices can be toggled by the memristor initial state, well reflecting the adaptive regulation of the memristor. Additionally, kinetic experiments on field programmable gate array (FPGA) verify the hardware implementability of DM-HNN, based on which an innovative memristor-state-based image encryption scheme is proposed, enabling resource-constrained scenarios and demonstrating excellent encryption performance.