Lotka-Volterra equations capture large-scale population activity in balanced random networks
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1
Bernstein Center Freiburg & Faculty of Biology, University of Freiburg, Germany
We study the rate dynamics of a sparsely connected recurrent network comprising excitatory and inhibitory neurons [1,3]. We describe its population dynamics by a system of Lotka-Volterra equations, which represent the mean-field equations for interacting populations of perfect integrators with exponential escape noise [2]. Here, we investigate how well this system of coupled nonlinear differential equations, and variants that can account for the membrane leak, reflects the large-scale dynamics of the network. Specifically, we attempt to identify the parameters of such a system from simulated activity in recurrent networks of leaky integrate-and-fire neurons, assess the goodness-of-fit, and compare the fitted parameters with the values obtained in an analytical approximation.
Previous work on such networks demonstrated that, depending on its parameters, several different activity states are displayed: synchronous regular (SR), asynchronous regular (AR), and asynchronous irregular (AI) activity [1]. The analysis was based on a diffusion approximation of input integration in single-neurons and a self-consistent mean-field description using a PDE-based Fokker-Planck formalism. We found that a bifurcation analysis based on coupled nonlinear ODEs leads to compatible results. In particular, we considered the relative strength of recurrent inhibition as a bifurcation parameter, which changes the excitation-inhibition balance. Another bifurcation parameter is the strength of external input, which is effective to induce AR states if synaptic delays are short.
Our analysis represents a first step toward analyzing the dynamics of more complex “networks of networks” that are implicated in various cognitive abilities of the brain.
Acknowledgements
Support by the German Federal Ministry of Education and Research (BMBF; grant 01GQ0420 to BCCN Freiburg) is gratefully acknowledged.
References
1. Brunel N. Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. Journal of Computational Neuroscience 8(3): 183-208, 2000
2. Cardanobile S, Rotter S. Multiplicatively interacting point processes and applications to neural modeling. Journal of Computational Neuroscience 28(2): 267-284, 2010
3. Ledoux E, Brunel N. Dynamics of networks of excitatory and inhibitory neurons in response to time-dependent inputs. Frontiers in Computational Neuroscience 5:25, 2011
Keywords:
Integrate and fire model,
large scale dynamics,
Lotka-Volterra equations,
Neurons,
networks,
and dynamical systems
Conference:
BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011, Freiburg, Germany, 4 Oct - 6 Oct, 2011.
Presentation Type:
Poster
Topic:
neurons, networks and dynamical systems (please use "neurons, networks and dynamical systems" as keywords)
Citation:
Lagzi
F,
Cardanobile
S and
Rotter
S
(2011). Lotka-Volterra equations capture large-scale population activity in balanced random networks.
Front. Comput. Neurosci.
Conference Abstract:
BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011.
doi: 10.3389/conf.fncom.2011.53.00167
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Received:
22 Aug 2011;
Published Online:
04 Oct 2011.
*
Correspondence:
Miss. Fereshteh Lagzi, Bernstein Center Freiburg & Faculty of Biology, University of Freiburg, Freiburg, Germany, fereshteh.lagzi@bcf.uni-freiburg.de