Origin of Chaos in a Two-Dimensional Map Modelling Spiking-Bursting Neural Activity

Origin of chaos in a simple two-dimensional map model replicating the spiking and spikingbursting activity of real biological neurons is studied. The map contains one fast and one slow variable. Individual dynamics of fast subsystem of the map is characterized by two types of possible attractors: stable fixed point (replicating silence) and superstable limit cycle (replicating spikes). Coupling this subsystem with slow subsystem leads to generation periodic or chaotic spiking-bursting behavior. We study the bifurcation scenarios which reveal the dynamical mechanisms that lead to chaos in alternation of silence and spiking phases.