Stochastic FitzHugh–Nagumo neuron model with Gamma distributed delay kernel

The FitzHugh–Nagumo (FHN) model is an efficient and biologically plausible model for simulating neuronal dynamics. However, it lacks any inherent capability to appropriately integrate memory effects. In this study, a non-Markov stochastic neuron model is formulated as an extension of the FHN model by incorporating Gamma distributed delay kernel as the form of memory in a recovery variable. Additionally, we propose an enhanced framework to incorporate neuronal noise into this model, further improving its ability to describe the propagation of action potential spikes along axons. We simulate the action potential signals recorded from the rat cortex by employing the modified version of the FHN model. This is done by constructing the input impulse signal from the recorded action potential data based on the time and quality of the action potential. This impulse signal is fed as input in the modified FHN model resulting in the replication of firing patterns of rat cortex, effectively replicate the action potential signals along with incorporating the inherent noise present in the recordings. This demonstrates the ability of the modified FHN model to accurately capture the dynamics of neuronal activity.