Pre-Driven and Post-Gated Memristive Hopfield Network: Dynamics, FPGA Realization and Image Encryption

Many existing memristive synaptic models merge presynaptic and postsynaptic activities into a single aggregated stimulus, making their distinct functional roles difficult to interpret. To address this issue, this paper proposes a memristive synapse with a pre-driven and post-gated state-update mechanism, in which presynaptic activity drives synaptic-state evolution while postsynaptic activity nonlinearly modulates the direction and strength of the update. The proposed synapse is embedded into a compact two-neuron memristive Hopfield neural network to investigate how this functional decomposition influences network dynamics. Equilibrium and stability analysis, bifurcation diagrams, Lyapunov exponents, and multistability analysis reveal variable-wing chaotic attractors, parameter-dependent transitions, and coexisting dynamical states. FPGA implementation verifies the hardware realizability of the proposed system, while a color-image encryption scheme demonstrates the application potential of the generated chaotic sequences. These results show that the proposed framework provides a functionally interpretable modeling route for incorporating differentiated pre/post synaptic regulation into memristive Hopfield dynamics.