Fractional-order Izhikevich neuron Model: PI-rules numerical simulations and parameter identification

This work introduces a novel approach to identifying parameters of the fractional-order (FO) Izhikevich spiking neuron model using real neuronal data. The primary contributions include the development of a limited memory numerical simulation scheme based on the modified Product-Integration Rectangular rule and the application of the Marine Predator Algorithm (MPA) to solve the nonlinear optimization problem of parameter identification. Experimental results demonstrate that the fractional-order neuron models significantly outperform the traditional integer-order models, as evidenced by higher median coincidence factors across multiple datasets. Specifically, the fractional-order models with smaller window sizes achieved superior performance, suggesting their potential for more accurate modeling of complex neuronal dynamics. This work paves the way for further exploration of fractional-order models in computational neuroscience, offering enhanced flexibility and precision in simulating neuronal behavior.