Asymptotic behavior of irreducible excitatory networks of analog graded-response neurons

In irreducible excitatory networks of analog graded-response neurons, the trajectories of most solutions tend to the equilibria. We derive sufficient conditions for such networks to be globally asymptotically stable. When the network possesses several locally stable equilibria, their location in the phase space is discussed and a description of their attraction basin is given. The results hold even when interunit transmission is delayed.