Lotka-Volterra Models Describe Large-Scale Activity of Balanced Random Networks

Abstract

Event Abstract Back to Event Lotka-Volterra Models Describe Large-Scale Activity of Balanced Random Networks Fereshteh Lagzi1, 2* and Stefan Rotter1, 2 1 Bernstein Center Freiburg, Germany 2 University of Freiburg, Faculty of Biology, Germany The large-scale dynamics of a balanced random network of excitatory and inhibitory integrate-and-fire neurons is the focus of our study. Based on the dynamical equations of the model, a mean field approach was employed to reduce the dimensionality of the network dynamics [1,2]. We analyzed the joint activity dynamics of excitatory and inhibitory populations using a pair of mutually interacting differential equations. In absence of a voltage leak for individual neurons, and for negligible synaptic transmission delay, these equations take the form of Lotka-Volterra equations. These are known for describing predator-prey systems, which correspond to excitatory and inhibitory populations in our case. We tried to find optimal parameters for the non-autonomous differential equations given a dataset from a numerical simulations of a network. Moreover, we attempted to analytically infer the parameters and compare it with the statistical estimates. As a next step, we analyzed the stability of the network considering two bifurcation parameters: “g”, the relative strength of recurrent inhibition, which controls the balance between excitation and inhibition in the network, and “eta”, the intensity of external input to the network. We found out that for a value of “g” that keeps the exact balance between excitation and inhibition, a bifurcation from unstable to stable network dynamics takes place. This bifurcation separates Synchronous Regular (SR) from Asynchronous Irregular (AI) activity of the network, similar to what was found in a previous study on the same network using a Fokker-Planck approach [3]. It has been shown that Lotka-Volterra equations are capable of representing switching dynamics between different states of neural networks [4]. 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).