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  • Poster presentation
  • Open Access

Dynamics of competition between coupled spiking networks in the balanced state

BMC Neuroscience201516 (Suppl 1) :P211

  • Published:


  • Phase Portrait
  • Stochastic Differential Equation
  • Neuronal Network
  • Network Activation
  • Connection Weight

The nonlinear mean-field dynamics of spiking neuronal networks with non-homogeneous connectivity is studied numerically and analyzed mathematically. The network under study is comprised of three subnetworks of either excitatory or inhibitory leaky integrate-and-fire neurons, two of which are of the same type. The excitatory and inhibitory weights are arranged to establish and maintain a balance between excitation and inhibition for a constant external drive. Each subnetwork has random connectivity with fixed in-degree and fixed out-degree for all neurons belonging to a particular population (configuration model). Neurons are also randomly connected with the same probability across different subnetworks; however, depending on their identity, the connection weight is scaled by a common factor. We observed that for a certain regime of ratios of the "within" versus "between" connection weights (bifurcation parameter), network activation spontaneously switches between the two subnetworks of the same identity. In the mean-field model, this phenomenon is explained by a set of coupled stochastic differential equations of Lotka-Volterra type [1, 2] that establish competition between the subnetworks. The model shows the same dynamical behavior as observed in simulations of large spiking networks.

The deterministic phase portrait is characterized by two attractors and a saddle node, its stochastic component is essentially given by the multiplicative inherent noise of the system [3]. We observe that the life time distribution of the active states is exponential, therefore, and it appears that noise fluctuations kicks the system from one attractor to the other. The same model for a larger number of populations suggests a general approach to study the dynamics of interacting populations of spiking networks.



This work was supported by the German Ministry of Education and Research (BFNT Freiburg*Tübingen, grant 01GQ0830) and the German Research Foundation (DFG, grant EXC 1086). This work was performed on the computational resource bwUniCluster funded by the Ministry of Science, Research and Arts and the Universities of the State of Baden-Württemberg, Germany, within the framework program bwHPC.

Authors’ Affiliations

Bernstein Center Freiburg, Freiburg, Germany
Faculty of Biology, University of Freiburg, Freiburg, Germany


  1. Lotka AJ: Analytical note on certain rhytmic relations in organic systems. PNAS. 1920, 6 (7): 410-415.PubMedPubMed CentralView ArticleGoogle Scholar
  2. Volterra V: Variations and Fluctuations of the Number of Individuals in Animal Species living together. Edited by: Chapman, R.N. 1931, McGrawHillGoogle Scholar
  3. Lagzi F, Rotter S: A Markov model for the temporal dynamics of balanced random networks of finite size. Frontiers in Computational Neuroscience. 2014, 8: 1-23.View ArticleGoogle Scholar


© Lagzi and Rotter 2015

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. The Creative Commons Public Domain Dedication waiver ( applies to the data made available in this article, unless otherwise stated.