In this paper, we studied neural networks of both excitatory and inhibitory populations with inhibition stabilized network (ISN) models. In ISN models, the recurrent excitatory connections are so strong that the excitatory sub-network is unstable if the inhibitory firing rate is fixed; however, the entire network is stable due to inhibitory connections. In such networks, external input to inhibitory neurons reduced their responses due to the withdrawal of network excitation (Tsodyks et al., 1997). This paradoxical effect of the ISN was observed in recent surround suppression experiments in the primary visual cortex with direct membrane conductance measurements (Ozeki et al., 2009). In our work, we used a linearized rate model of both excitatory and inhibitory populations with weight matrices dependent on the locations of the neurons. We applied this model to study surround suppression effects and searched for networks with appropriated parameters. The same model was also applied in the study of spontaneous activities in awake ferrets.

Both studies led to network solutions in the ISN regime, suggesting that ISN mechanisms might play an important role in the neural circuitry in the primary visual cortex.