Consiglio Nazionale delle Ricerche

Tipo di prodottoArticolo in rivista
TitoloVery long transients, irregular firing, and chaotic dynamics in networks of randomly connected inhibitory integrate-and-fire neurons
Anno di pubblicazione2009
Autore/iZillmer R.; Brunel N.; Hansel D.
Affiliazioni autori1) Laboratoire de Neurophysique et Physiologie, Université Paris Descartes, 75270 Paris Cedex 06, France 2) CNRS, UMR 8119, 45 rue des Saints Pères, 75270 Paris Cedex 06, France 3) Istituto dei Sistemi Complessi, CNR via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
Autori CNR e affiliazioni
AbstractWe present results of an extensive numerical study of the dynamics of networks of integrate-and-fire neurons connected randomly through inhibitory interactions. We first consider delayed interactions with infinitely fast rise and decay. Depending on the parameters, the network displays transients which are short or exponentially long in the network size. At the end of these transients, the dynamics settle on a periodic attractor. If the number of connections per neuron is large (?1000), this attractor is a cluster state with a short period. In contrast, if the number of connections per neuron is small (?100), the attractor has complex dynamics and very long period. During the long transients the neurons fire in a highly irregular manner. They can be viewed as quasistationary states in which, depending on the coupling strength, the pattern of activity is asynchronous or displays population oscillations. In the first case, the average firing rates and the variability of the single-neuron activity are well described by a mean-field theory valid in the thermodynamic limit. Bifurcations of the long transient dynamics from asynchronous to synchronous activity are also well predicted by this theory. The transient dynamics display features reminiscent of stable chaos. In particular, despite being linearly stable, the trajectories of the transient dynamics are destabilized by finite perturbations as small as O(1/N). We further show that stable chaos is also observed for postsynaptic currents with finite decay time. However, we report in this type of network that chaotic dynamics characterized by positive Lyapunov exponents can also be observed. We show in fact that chaos occurs when the decay time of the synaptic currents is long compared to the synaptic delay, provided that the network is sufficiently large.
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Pagine da031909
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Numero volume della rivista79(3)
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Parole chiaveNeural networks
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Strutture CNR
  • ISC — Istituto dei sistemi complessi
Moduli/Attività/Sottoprogetti CNR
  • MD.P02.017.001 : comportamento dinamico di sistemi complessi
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Area disciplinarePhysics
Area valutazione CIVRScienze fisiche