ERVIS GEGA, ELDA SPAHIU, KLAUDIA KAÇORI
Abstract
Potential oscillation in neurons is quite well-known and presents its own challenges in in-depth studies of the theoretical models proposed by different researchers. The self-contained oscillatory behaviour of the neuron’s potential after an external stimulus as well as other bifurcation phenomena add to the need for the analysis of the nonlinear dynamics of the modelled system by advancing to computer simulations for different values of the stimulus magnitude, enabling a systematic investigation of the parameter space of mathematical models. Numerical integrations and computer simulations provide clear insight about the behaviour of the complicated systems, pointing out various phenomena such as changes in the stability of systems. Neuronal membrane potential oscillations represent a well-known nonlinear phenomenon where bifurcations and other nonlinearity phenomena appear for different values of the control parameter. In the following, the time series, phase space, parameter space and bifurcation diagrams will be presented for the basic mathematical models of neurons such as the Fitzhugh-Nagumo (FN) and Hodgkin-Huxley (HH) models, and other more advanced models will be attempted.
Key words: Neuronal oscillation, nonlinear dynamics, bifurcation, numerical simulation.