#### Stefano Luccioli (Istituto dei Sistemi Complessi, Firenze, Italy)

# Emergence of irregular collective oscillations in a neuronal network model

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#### Abstract

We consider a network of pulse-coupled leaky-integrate-and-fire neurons. We show that, changing the structure of the network, regimes with different dynamical complexity are observed. In particular, we focus on the case of neurons characterized by a distribution of spiking frequencies, i.e. in a setup similar to that of the Kuramoto model.

We see that, upon increasing the coupling strength, the network exhibits a transition from an asynchronous regime to a nontrivial collective behavior. There are relevant differences with the Kuramoto model.

1) First, the dynamics is not chaotic, it eventually converges to a periodic orbit, and the transient time needed to approach the orbit grows exponentially with the number of neurons (this is an instance of the dynamical regime called ?stable chaos?).

2) Moreover, the most striking and interesting feature is that the overall macroscopic neural activity shows irregular, seemingly chaotic, oscillations for very large system size.

References

[1] S. Luccioli and A. Politi, Phys. Rev. Lett. 105, 158104 (2010).

[2] A. Politi and S. Luccioli, Dynamics of networks of

leaky-integrate-and-fire neurons, in Network Science, Eds. E. Estrada,

M. Fox, D. Higham and G.L. Oppo (Springer-Verlag, London, 2010)