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Several firing patterns experimentally observed in neural populations havebeen successfully correlated to animal behavior. Population bursting, herebyregarded as a period of high firing rate followed by a period of quiescence, istypically observed in groups of neurons during behavior. Biophysicalmembrane-potential models of single cell bursting involve at least threeequations. Extending such models to study the collective behavior of neuralpopulations involves thousands of equations and can be very expensivecomputationally. For this reason, low dimensional population models thatcapture biophysical aspects of networks are needed.  \noindent The present paper uses a firing-rate model to study mechanisms thattrigger and stop transitions between tonic and phasic population firing. Thesemechanisms are captured through a two-dimensional system, which can potentiallybe extended to include interactions between different areas of the nervoussystem with a small number of equations. The typical behavior of midbraindopaminergic neurons in the rodent is used as an example to illustrate andinterpret our results.  \noindent The model presented here can be used as a building block to studyinteractions between networks of neurons. This theoretical approach may helpcontextualize and understand the factors involved in regulating burst firing inpopulations and how it may modulate distinct aspects of behavior.

Mechanisms explaining transitions between tonic and phasic firing in neuronal populations as predicted by a low dimensional firing rate model