Modeling of spiking-bursting neural behavior using two-dimensional map

A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map that contains one fast and one slow variable. The mechanisms behind generation of spikes, bursts of spikes, and restructuring of the map behavior are explained using phase portrait analysis. The dynamics of two coupled maps that model the behavior of two electrically coupled neurons is discussed. Synchronization regimes for spiking and bursting activities of these maps are studied as a function of coupling strength. It is demonstrated that the results of this model are in agreement with the synchronization of chaotic spiking-bursting behavior experimentally found in real biological neurons.