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Very long transients, irregular firing, and chaotic dynamics in networks of randomly connected inhibitory integrate-and-fire neurons.

Publication ,  Journal Article
Zillmer, R; Brunel, N; Hansel, D
Published in: Phys Rev E Stat Nonlin Soft Matter Phys
March 2009

We 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 ( approximately 1000) , this attractor is a cluster state with a short period. In contrast, if the number of connections per neuron is small ( approximately 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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Published In

Phys Rev E Stat Nonlin Soft Matter Phys

DOI

ISSN

1539-3755

Publication Date

March 2009

Volume

79

Issue

3 Pt 1

Start / End Page

031909

Location

United States

Related Subject Headings

  • Time Factors
  • Thermodynamics
  • Synapses
  • Neurons
  • Nerve Net
  • Models, Neurological
  • Membrane Potentials
  • Fluids & Plasmas
  • 09 Engineering
  • 02 Physical Sciences
 

Citation

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Zillmer, R., Brunel, N., & Hansel, D. (2009). Very long transients, irregular firing, and chaotic dynamics in networks of randomly connected inhibitory integrate-and-fire neurons. Phys Rev E Stat Nonlin Soft Matter Phys, 79(3 Pt 1), 031909. https://doi.org/10.1103/PhysRevE.79.031909
Zillmer, Rüdiger, Nicolas Brunel, and David Hansel. “Very long transients, irregular firing, and chaotic dynamics in networks of randomly connected inhibitory integrate-and-fire neurons.Phys Rev E Stat Nonlin Soft Matter Phys 79, no. 3 Pt 1 (March 2009): 031909. https://doi.org/10.1103/PhysRevE.79.031909.
Zillmer R, Brunel N, Hansel D. Very long transients, irregular firing, and chaotic dynamics in networks of randomly connected inhibitory integrate-and-fire neurons. Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Mar;79(3 Pt 1):031909.
Zillmer, Rüdiger, et al. “Very long transients, irregular firing, and chaotic dynamics in networks of randomly connected inhibitory integrate-and-fire neurons.Phys Rev E Stat Nonlin Soft Matter Phys, vol. 79, no. 3 Pt 1, Mar. 2009, p. 031909. Pubmed, doi:10.1103/PhysRevE.79.031909.
Zillmer R, Brunel N, Hansel D. Very long transients, irregular firing, and chaotic dynamics in networks of randomly connected inhibitory integrate-and-fire neurons. Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Mar;79(3 Pt 1):031909.

Published In

Phys Rev E Stat Nonlin Soft Matter Phys

DOI

ISSN

1539-3755

Publication Date

March 2009

Volume

79

Issue

3 Pt 1

Start / End Page

031909

Location

United States

Related Subject Headings

  • Time Factors
  • Thermodynamics
  • Synapses
  • Neurons
  • Nerve Net
  • Models, Neurological
  • Membrane Potentials
  • Fluids & Plasmas
  • 09 Engineering
  • 02 Physical Sciences