Bursting regimes in map-based neuron models coupled through fast threshold modulation

A system consisting of two map-based neurons coupled through reciprocal excitatory or inhibitory chemical synapses is discussed. After a brief explanation of the basic mechanism behind generation and synchronization of bursts, parameter space is explored to determine less obvious but biologically meaningful regimes and effects. Among them, we show how excitatory synapses without any delays may induce antiphase synchronization; that a synapse may change its character from excitatory to inhibitory and vice versa by changing its conductance, without any change in reversal potential; and that small variations in the synaptic threshold may result in drastic changes in the synchronization of spikes within bursts. Finally we show how the synchronization effects found in the two-neuron system carry over to larger networks.