Abstract
The study of balanced networks of excitatory and inhibitory neurons has led to several open questions. On the one hand it is yet unclear whether the asynchronous state observed in the brain is autonomously generated, or if it results from the interplay between external drivings and internal dynamics. It is also not known, which kind of network variabilities will lead to irregular spiking and which to synchronous firing states. Here we show how isolated networks of purely excitatory neurons generically show asynchronous firing whenever a minimal level of structural variability is present together with a refractory period. Our autonomous networks are composed of excitable units, in the form of leaky integrators spiking only in response to driving currents, remaining otherwise quiet. For a non-uniform network, composed exclusively of excitatory neurons, we find a rich repertoire of self-induced dynamical states. We show in particular that asynchronous drifting states may be stabilized in purely excitatory networks whenever a refractory period is present. Other states found are either fully synchronized or mixed, containing both drifting and synchronized components. The individual neurons considered are excitable and hence do not dispose of intrinsic natural firing frequencies. An effective network-wide distribution of natural frequencies is however generated autonomously through self-consistent feedback loops. The asynchronous drifting state is, additionally, amenable to an analytic solution. 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 of the drifting component, however, becomes irregular in the mixed state, due to the periodic driving of the synchronized component. We propose a new tool for the study of chaos in spiking neural networks, which consists of an analysis of the time series of pairs of consecutive interspike intervals. In this space, we show that a strange attractor with a fractal dimension of about 1.8 is formed in the mentioned mixed state.
Highlights
The study of collective synchronization has attracted the attention of researchers across fields for over half a century (Winfree, 1967; Kuramoto, 1975; Peskin, 1975; Buck, 1988; Pikovsky and Rosenblum, 2015)
We characterize how the features of the network dynamics depend on the coupling properties of the network and, in particular, we explore the possibility of chaos in the here studied case of excitable units, when partial synchrony is present, since this link has already been established in the case of coupled oscillators with a distribution of natural frequencies (Miritello et al, 2009), while other studies had shown how stable chaos emerges in inhibitory networks of homogeneous connection statistics (Angulo-Garcia and Torcini, 2014)
In the current work we study the properties of the selfinduced stationary dynamical states in autonomous networks of excitable integrate-and-fire neurons
Summary
The study of collective synchronization has attracted the attention of researchers across fields for over half a century (Winfree, 1967; Kuramoto, 1975; Peskin, 1975; Buck, 1988; Pikovsky and Rosenblum, 2015). One can use phase coupling methods to study networks of pulse coupled oscillators (Mirollo and Strogatz, 1990; Kuramoto, 1991; Izhikevich, 1999), by establishing a map between the internal state variable V and a periodic phase φ given by the state of the unit within its limit cycle. We characterize how the features of the network dynamics depend on the coupling properties of the network and, in particular, we explore the possibility of chaos in the here studied case of excitable units, when partial synchrony is present, since this link has already been established in the case of coupled oscillators with a distribution of natural frequencies (Miritello et al, 2009), while other studies had shown how stable chaos emerges in inhibitory networks of homogeneous connection statistics (Angulo-Garcia and Torcini, 2014)
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