Fractional Spiking Neuron: Fractional Leaky Integrate-and-Fire Circuit Described with Dendritic Fractal Model

As dendrites are essential parts of neurons, they are crucial factors for neuronal activities to follow multiple timescale dynamics, which ultimately affect information processing and cognition. However, in the common SNN (Spiking Neural Networks), the hardware-based LIF (Leaky Integrate-and-Fire) circuit only simulates the single timescale dynamic of soma without relating dendritic morphologies, which may limit the capability of simulating neurons to process information. This study proposes the dendritic fractal model mainly for quantifying dendritic morphological effects containing branch and length. To realize this model, We design multiple analog fractional-order circuits (AFCs) which match their extended structures and parameters with the dendritic features. Then introducing AFC into FLIF (Fractional Leaky Integrate-and-Fire) neuron circuits can demonstrate the same multiple timescale dynamics of spiking patterns as biological neurons, including spiking adaptation, inter-spike variability with power-law distribution, first-spike latency, and intrinsic memory. By contrast, it further enhances the degree of mimicry of neuron models and provides a more accurate model for understanding neural computation and cognition mechanisms.