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The study of balanced networks of excitatory and inhibitory neurons has ledto several open questions. On the one hand it is yet unclear whether theasynchronous state observed in the brain is autonomously generated, or if itresults from the interplay between external drivings and internal dynamics. Itis also not known, which kind of network variabilities will lead to irregularspiking and which to synchronous firing states. Here we show how isolatednetworks of purely excitatory neurons generically show asynchronous firingwhenever a minimal level of structural variability is present together with arefractory period. Our autonomous networks are composed of excitable units, inthe form of leaky integrators spiking only in response to driving inputs. For anon-uniform network, composed exclusively of excitatory neurons, we find a richrepertoire of self-induced dynamical states, including asynchronous driftingstates, fully synchronized, or mixed, containing both drifting and synchronizedcomponents. The individual neurons considered are excitable and hence do notdispose of intrinsic natural firing frequencies. An effective network-widedistribution of natural frequencies is however generated autonomously throughself-consistent feedback loops. We find two types of asynchronous activity,with the individual neurons spiking regularly in the pure drifting state,albeit with a continuous distribution of firing frequencies. The activity ofthe drifting component, however, becomes irregular in the mixed state, due tothe periodic driving of the synchronized component. We propose a new tool forthe study of chaos in spiking neural networks, which consists of an analysis ofthe time series of pairs of consecutive interspike intervals. In this space, weshow that a strange attractor with a fractal dimension is formed.

Drifting states and synchronization induced chaos in autonomous networks of excitable neurons