Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons

The dynamics of networks of sparsely connected excitatory and inhibitory in tegrate-and-fire neurons are studied analytically. The analysis reveals a r ich repertoire of states, including synchronous states in which neurons fir e regularly; asynchronous states with stationary global activity and very i rregular individual cell activity; and slates in which the global activity oscillates but individual cells fire irregularly, typically at rates lower than the global oscillation frequency. The network can switch between these states, provided the external frequency, or the balance between excitation and inhibition, is varied. Two types of network oscillations are observed. In the fast oscillatory state, the network frequency is almost fully contr olled by the synaptic time scale. In the slow oscillatory state, the networ k frequency depends mostly on the membrane time constant. Finite size effec ts in the asynchronous state are also discussed.