| Summary: | Computational models at different spacetime scales allow us to understand the fundamentalmechanisms that govern neural processes and relate uniquely these processes to neurosciencedata. In this work, we propose a novel neurocomputational unit (a mesoscopic model whichtell us about the interaction between local cortical nodes in a large scale neural mass model)of bursters that qualitatively captures the complex dynamics exhibited by a full network ofparabolic bursting neurons. We observe that the temporal dynamics and fluctuation of meansynaptic action term exhibits a high degree of correlation with the spike/burst activity ofour population. With heterogeneity in the applied drive and mean synaptic coupling derivedfrom fast excitatory synapse approximations we observe long term behavior in our populationdynamics such as partial oscillations, incoherence, synchrony. In order to understand theorigin of multistability at the population level as a function of mean synaptic coupling andheterogeneity in the firing rate threshold we employ a simple generative model for parabolicbursting recently proposed by Ghosh, Roy & Jirsa (2009). Further, we use here a meancoupling formulated for fast spiking neurons for our analysis of generic model. Stabilityanalysis of this mean field network allow us to identify all the relevant network states foundin the detailed biophysical model. We derive here analytically several boundary solutions, aresult which holds for any number of spikes per burst. These findings illustrate the role ofoscillations occurring at slow time scales (bursts) on the global behavior of the network.
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