A novel chaotic Hopfield neural network with memristor-driven excitation and threshold-based activation functions

Abstract In conventional Hopfield neural networks(HNN), external input currents are typically modeled using preset functions, which cannot effectively represent the diversity and complexity of real-world external stimuli. Moreover, existing studies rarely consider neuron-specific activation thresholds or region-dependent neuronal activity levels. To overcome these limitations, we propose a Memristor-driven incentive current Hopfield neural network(MIC-HNN) that integrates a novel voltage-controlled memristor model and threshold-based activation functions. The memristor simultaneously generates external incentive currents and mediates inter-neuronal signal transmission, while the threshold mechanism introduces heterogeneity in neuronal excitability. The proposed MIC-HNN exhibits complex dynamical behaviors including multistability, multiple attractors, and high-dimensional chaos. Importantly, the number and spatial distribution of attractors can be flexibly tuned by adjusting a single memristor parameter. Furthermore, the nonlinear interaction between incentive currents and memristor dynamics enables the generation of multi-scroll chaotic attractors, further enriching the system dynamics. Numerical simulations verify the robustness and adaptability of MIC-HNN in capturing neuronal activity diversity. Compared with traditional HNN, the proposed framework provides a circuit-level scheme for precise controllability of network dynamics and establishes a practical modeling approach for neuromorphic computing.