Astrocyte-mediated Hopfield Neural Network: modeling, dynamical analysis, and hardware implementation

Astrocytes actively participate in neural information processing and modulate multiple surrounding neurons through a “one-to-many” regulatory mechanism. To explore this interaction, we propose an astrocyte-mediated Hopfield neural network (AmHNN) model that captures the essential coupling structure of biological neural networks. Linear stability analysis reveals that astrocyte feedback can shift the network's equilibrium point, thereby modifying the Jacobian matrix and its eigenvalues. This reshapes the network's stability landscape and provides a theoretical basis for the emergence of complex rhythms, including chaos and hyper-chaos. Comparative analysis with models lacking the astrocyte or the third neuron indicates that AmHNN is not merely an expansion of the network dimension; its rich dynamic characteristics better mimic the firing rhythm of biological neural networks. By tuning astrocyte feedback intensities and internal parameters, we quantitatively characterize astrocyte-induced variations in network stability and derive a Hamiltonian energy function. This reveals how astrocyte feedback modulates the rate and magnitude of energy injection to drive transitions in network firing dynamics. A DSP-based hardware implementation, evaluated using a multidimensional framework involving NRMSE and Pearson correlation, demonstrates strong agreement with numerical simulations. These findings deepen the deepen understanding of neuron-astrocyte interactions, thereby offering a novel paradigm for advancing neuromorphic computing, secure communications, and brain-inspired intelligence.