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We present a mean field solution of the dynamics of a Greenberg-Hastingsneural network with both excitatory and inhibitory units. We analyse thedynamical phase transitions that appear in the stationary state as the modelparameters are varied. Analytical solutions are compared with numericalsimulations of the microscopic model defined on a fully connected network. Wefound that the stationary state of this system exhibits a first order dynamicalphase transition (with the associated hysteresis) when the fraction ofinhibitory units $f< f_t \leq 1/2$, even for a finite system. In finitesystems, when $f > f_t$ the first order transition is replaced by a pseudocritical one, namely a continuous crossover between regions of low and highactivity that resembles the finite size behaviour of a continuous phasetransition order parameter. However, in the thermodynamic limit, we found that$f_t\to 1/2$ and the activity for $f\geq f_t$ becomes negligible for any valueof $T>0$, while the first order transition for $f<f_t$ remains.

Mean-field solution of the neural dynamics in a Greenberg-Hastings model with excitatory and inhibitory units