Using Series Expansion Instead of Nonlinear Function in FPGA Implementation of Memristive Hindmarsh–Rose Neuron Model

In this study, the three-dimensional Memristive Hindmarsh-Rose (MHR) neuron model is investigated. This model is a variant of the Hindmarsh-Rose (HR) model, a wellestablished framework for modeling neuronal dynamics, and it is extended by incorporating a memristor. The nonlinear function in the original equation, representing the effect of electromagnetic induction, poses challenges for hardware implementation on certain platforms. In this work, the function is simplified using Taylor-Maclaurin series expansion, enhancing the model’s suitability for hardware realization. The behaviors of the original and simplified models are compared by calculating root mean square (RMS) error, phase error, and correlation coefficients. To demonstrate the hardware implementability, the MHR model was discretized using the Euler method and successfully implemented on an FPGA platform. The results, including time series, phase portraits, and resource utilization metrics, are also presented.