Can neuron change from excitatory to inhibitory (and vice versa) over time? According to this answer a neuron can release only specific type of neurotransmitters at the time, however, could it change over time? For example a neuron that now releases only inhibitory neurotransmitters, after a few days will turn into a neuron releasing only excitatory neurotransmitters. If it is possible, then what does it depend on (mathematical models appreciated)?
As far as I know, it is not possible for a neuron to change which type of neurotransmitter it releases.  However, it is the case that the neurotransmitter GABA changes from excitatory to inhibitory over the course of development.  This is occurs because GABA activates Cl- (chloride) channels.  The chloride concentration gradient across the cell membrane changes directions over development, so the direction of current caused by opening of Cl- channels also changes.  

Nature Reviews Neuroscience 3, 728-739 (September 2002) | doi:10.1038/nrn920
Excitatory actions of gaba during development: the nature of the nurture
Yehezkel Ben-Ari
http://www.nature.com/nrn/journal/v3/n9/abs/nrn920.html