The FitzHugh-Nagumo model: Firing modes with time-varying parameters and parameter estimation

In this paper, we revisit the issue of the utilityof the FitzHugh-Nagumo (FHN) model for capturing neuronfiring behaviors. It has been noted (e.g., see [6]) that theFHN model cannot exhibit certain interesting firing behaviorssuch as bursting. We illustrate that, by allowing time-varyingparameters for the FHN model, one could overcome suchlimitations while still retaining the low order complexity ofthe FHN model. We also highlight the utility of the FHN modelfrom an estimation perspective by presenting a novel parameterestimation method that exploits the multiple time scale featureof the FHN model, and compare the performance of this methodwith the Extended Kalman Filter through illustrative examples.