Numerical Effects in Computer Simulation of Simplified Hodgkin-huxley Model

In this paper, we consider the impact of the discretization effects on the dynamical behaviour of the single-compartment neuron model represented by simplified Hodgkin-Huxley equations. In order to implement numerical simulation, one need to discretize the continuous model of the system or use the discrete operator preserving the main properties of the continuous prototype. However, discrete models can suffer from negative effects caused by the applied method, discretization step and round-off errors. This fact is particularly important for the analysis of nonlinear systems, e.g. the biological neuron models. Within this study, the impact of the application of the most common one-step integration methods is examined through the series of computational experiments, where the dynamical system is put into the resonant and chaotic oscillation modes. The results of the study are visualized as two-parameter dynamical maps and interspike interval histograms.