Meminductor synaptic coupling in a heterogeneous HR–FHN neuron network: Model, dynamics, and DSP implementation

To functionally emulate the history-dependent plasticity and electromagnetic induction effects inherent in biochemical synapses, this paper proposes a heterogeneous neural network model in which Hindmarsh–Rose (HR) neurons and FitzHugh–Nagumo (FHN) neurons are coupled via a synaptic connection composed of a meminductor in series with a resistor. This architecture explicitly decouples synaptic function: the linear resistor models the instantaneous conductive pathway, while the meminductor implements the history-dependent plastic pathway. The complex firing dynamics of the coupled system are systematically investigated through bifurcation diagrams, Lyapunov exponent spectra, phase portraits, and time-series analysis. The results show that variations in synaptic coupling strength and coupling resistance can induce transitions between diverse firing patterns, including chaotic spiking, periodic bursting, and alternations between periodic and chaotic states. Crucially, the meminductive synapse introduces activity-dependent multistability, manifested as the coexistence of multiple firing patterns determined by its initial internal state. Phase synchronization analysis further demonstrates that adjusting the coupling resistance provides an independent control mechanism that effectively enhances or suppresses synchronous firing between the two heterogeneous neurons, even at a fixed coupling strength. Finally, the physical feasibility of the system is validated through successful digital implementation on a digital signal processor (DSP) platform, as experimental measurements show excellent agreement with numerical simulations. This study establishes the meminductor as a biomimetically grounded element for chemical synapse emulation and provides a dynamically rich, hardware-validated platform for neuromorphic computing and information processing.