We present a kinetic theory for all-to-all coupled networks of identical, linear, integrate-and-fire, excitatory point neurons in which a fast and a slow excitatory conductance are driven by the same spike train in the presence of synaptic failure. The maximal-entropy principle guides us in deriving a set of three (1+1) -dimensional kinetic moment equations from a Boltzmann-like equation describing the evolution of the one-neuron probability density function. We explain the emergence of correlation terms in the kinetic moment and Boltzmann-like equations as a consequence of simultaneous activation of both the fast and slow excitatory conductances and furnish numerical evidence for their importance in correctly describing the coarse-grained dynamics of the underlying neuronal network.
|Original language||English (US)|
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|State||Published - Apr 18 2008|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics