Skip to main content


  • Poster presentation
  • Open Access

Dynamics of self-sustained activity in random networks with strong synapses

  • 1Email author,
  • 1,
  • 1,
  • 2, 3 and
  • 1
BMC Neuroscience201112 (Suppl 1) :P89

  • Published:


  • Neural Network
  • Stochastic Model
  • Firing Rate
  • Network Size
  • Random Network
An understanding of short-term memory requires models of neural networks which are able to sustain activity in the absence of external input for several seconds. About half a century ago, [1] predicted the existence of self-sustained activity in neural networks with strong synapses. Despite this finding, most previous studies on the dynamics of neural networks are restricted to weak synapses, i.e. to a regime where the diffusion approximation is applicable. Recently, it has been shown in simulations that self-sustained activity emerges in networks of integrate-and-fire (IaF) neurons with strong synapses modeled as currents [2] (rather than as conductances, see [3]). Above a critical synaptic weight, the lifetime of self-sustained activity increases rapidly (Fig. 1C). We present a stochastic model of the dynamics of a balanced random network of IaF neurons with current-based synapses in the strong-synapse regime. Based on the network's firing-rate transfer [4], we show that the firing-rate dynamics becomes bistable if the synapses are sufficiently strong: in addition to the quiescent state, a second stable fixed point at moderate firing rates is created (sketched in Fig. 1A). Firing-rate fluctuations can destabilize this fixed point, thereby limiting the lifetime of self-sustained activity (sketched in Fig. 1B). The magnitude of these fluctuations is mainly determined by the amount of spike-train correlations [5]. Our model explains the existence and the lifetime of self-sustained activity, and how the lifetime depends on the network size, the connectivity, the level of inhibition and the synapse strength. The results of our model are confirmed by network simulations.
Figure 1
Figure 1

A. Phase space of the firing-rate dynamics. Dependence of the rate change dr/dt on the rate r (sketch). B. Firing-rate distribution in the self-sustained state (sketch). C. Dependence of the lifetime of self-sustained activity (color coded) on the level g of inhibition and the synaptic weight J in a random network of 100000 excitatory and 25000 inhibitory IaF neurons with 1% connectivity (simulation results).



We acknowledge support by the NOTUR and eScience programs of the Research Council of Norway. All network simulations were carried out with the neural simulation tool NEST (see

Authors’ Affiliations

Dept. of Mathematical Sciences and Technology, Norwegian University of Life Sciences, NO-1432 Ås, Norway
Honda Research Institute Europe GmbH, D-63073, Offenbach/Main, Germany
Bernstein Center for Computational Neuroscience, D-79104 Freiburg, Germany


  1. Griffiths JS: On the stability of brain-like structures. Biophys J. 1963, 3: 299-308. 10.1016/S0006-3495(63)86822-8.View ArticleGoogle Scholar
  2. Gewaltig M: Self-sustained activity in networks of integrate and fire neurons without external noise. Front. Comput. Neurosci. Conference Abstract: Bernstein Conference on Computational Neuroscience. 2009, doi: 10.3389/conf.neuro.10.2009.14.051Google Scholar
  3. Kuhn A, Aertsen A, Rotter S: Neuronal integration of synaptic input in the fluctuation-driven regime. J Neurosci. 2004, 24 (10): 2345-2356. 10.1523/JNEUROSCI.3349-03.2004.View ArticlePubMedGoogle Scholar
  4. Siegert AJF: On the first passage time probability problem. Phys Rev. 1951, 81: 617-623. 10.1103/PhysRev.81.617.View ArticleGoogle Scholar
  5. Kriener B, Tetzlaff T, Aertsen A, Diesmann M, Rotter S: Correlations and population dynamics in cortical networks. Neural Comput. 2008, 20: 2185-2226. 10.1162/neco.2008.02-07-474.View ArticlePubMedGoogle Scholar


© Enger et al; licensee BioMed Central Ltd. 2011

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.