# Dynamics of recurrent neural networks with delayed unreliable synapses: metastable clustering

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## Abstract

The influence of unreliable synapses on the dynamic properties of a neural network is investigated for a homogeneous integrate-and-fire network with delayed inhibitory synapses. Numerical and analytical calculations show that the network relaxes to a state with dynamic clusters of identical size which permanently exchange neurons. We present analytical results for the number of clusters and their distribution of firing times which are determined by the synaptic properties. The number of possible configurations increases exponentially with network size. In addition to states with a maximal number of clusters, metastable ones with a smaller number of clusters survive for an exponentially large time scale. An externally excited cluster survives for some time, too, thus clusters may encode information.

## Keywords

Neural networks Cluster Synchronization Integrate-and-fire neurons Pulse-coupled oscillators Unreliable synapses## Notes

### Acknowledgements

It is a pleasure for us to acknowledge stimulating and fruitful discussions with Ido Kanter and Moshe Abeles.

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