Parameters analysis of FitzHugh-Nagumo model for a reliable simulation

Derived from the pioneer ionic Hodgkin-Huxley model and due to its simplicity and richness from a point view of nonlinear dynamics, the FitzHugh-Nagumo model (FHN) is one of the most successful simplified neuron / cardiac cell model. There exist many variations of the original FHN model. Though these FHN type models help to enrich the dynamics of the FHN model, the parameters used in these models are often in biased conditions. The related results would be questionable. So, in this study, the aim is to find the parameter thresholds for one of the commonly used FHN model in order to provide a better simulation environment. The results showed at first that inappropriate time step and integration tolerance in numerical solution of FHN model can give some biased results which would make some publications questionable. Then the thresholds of parameters α, γ and ε are presented. α controls the global dynamics of FHN. α > 0, the cell is in refractory mode; α <; 0, the cell is excitable. ε controls the main morphology of the action potential generated and has a relation with the period (P = 3.065 × α_α,γ^-0.8275+ 4.397). To show oscillations of relaxation with FHN, ε should be smaller than 0.0085. 7 influences barely action potential, it showed linear relationship with the period and duration of action potential. Even though α <; 0.1, ε <; 0.0085, there is no definite threshold for γ, smaller values are recommended.