Multi-scroll memristive tabu learning neural network with saddle-type equilibria

Recent advancements in neuromorphic computing have fueled growing interest in constructing multi-scroll chaotic attractors using memristors and neurons. However, current approaches exhibit limitations in dynamic configurability and attractor complexity. To address this, we propose a tabu learning neural network with memristor-based synapses, uniquely distinguished by saddle-type equilibria. By strategically manipulating the logic levels of external excitation currents, multiple equilibrium points are configured, which in turn facilitate the formation of diversely distributed multi-scroll chaotic attractors with controllable equilibrium-point evolution paths. Furthermore, the memristor state equation allows for precise shaping of these equilibrium points, dictating the arrangement of attractors in phase space. Notably, the introduction of a piecewise-defined multistable memristor partitions the phase space into multiple stable sub-regions. This segmentation not only expands the network’s attraction region but also allows for the generation of multi-scroll attractors within each sub-region, a phenomenon we term “multi-multi-scroll dynamics”. FPGA-based hardware experiments validate the practical feasibility of our approach, while the developed pseudo-random number generator (PRNG) with enhanced complexity showcases the broad applicability of these generated attractors.