The aim of this work is to analyze theoretically and numerically the dynamics of a network of excitatory and inhibitory neurons of ordinary differential equations (ODE) of Hodgkin-Huxley type (HH) inspired by the primary visual cortex V1. The model emphasizes an approach combining a driven stochastic drive for each neuron and recurrent inputs resulting from the network activity. After a review of the dynamics of a single HH equation, for both deterministic and stochastic driven case, we proceed to the analysis of the network. Our numerical analysis highlights emergent properties such as partial synchronization and synchronization, waves of excitability, and oscillations in the gamma-band frequency.