Multi-scroll hyperchaotic memristor Hopfield neural network and application in enhanced image encryption

While multi-scroll attractor generation has been extensively investigated in conventional chaotic systems, the exploration of coupled multi-neuron neural networks and their brain-like chaotic dynamics remains limited. This work focuses on multi-directionally extended multi-scroll attractors in memristor-coupled Hopfield neural networks, proposing three novel models with single, dual, and triple memristive synapses. By replacing traditional synapses with multi-segment nonlinear memristors, a memristor-regulated network architecture is constructed, enabling stable generation and precise control of multi-scroll hyperchaotic attractors. Dynamical analysis using phase portraits, bifurcation diagrams, and Lyapunov exponents, as well as circuit simulations, validates the complex dynamics and physical realizability of the proposed system. On this basis, the hyperchaotic sequences generated by the multi-scroll memristive synapse Hopfield neural network are modeled and reconstructed by a long short-term memory (LSTM) network. The LSTM is treated as a new discrete dynamical system to generate chaos-based sequences with enhanced dynamical complexity, which are then applied to image encryption. Extensive tests confirm that the introduced chaotic system and LSTM-based dynamical reconstruction mechanism effectively improve key complexity, nonlinearity, and attack resistance compared with traditional chaotic encryption methods, showing high security and practical application potential.