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Emergent Oscillations in Networks of Stochastic Spiking Edward Wallace1
 

Summary: Emergent Oscillations in Networks of Stochastic Spiking
Neurons
Edward Wallace1
*.
, Marc Benayoun2.
, Wim van Drongelen2,3
, Jack D. Cowan1
1 Department of Mathematics, University of Chicago, Chicago, Illinois, United States of America, 2 Department of Pediatrics, University of Chicago, Chicago, Illinois, United
States of America, 3 Computation Institute, University of Chicago, Chicago, Illinois, United States of America
Abstract
Networks of neurons produce diverse patterns of oscillations, arising from the network's global properties, the propensity of
individual neurons to oscillate, or a mixture of the two. Here we describe noisy limit cycles and quasi-cycles, two related
mechanisms underlying emergent oscillations in neuronal networks whose individual components, stochastic spiking
neurons, do not themselves oscillate. Both mechanisms are shown to produce gamma band oscillations at the population
level while individual neurons fire at a rate much lower than the population frequency. Spike trains in a network undergoing
noisy limit cycles display a preferred period which is not found in the case of quasi-cycles, due to the even faster decay of
phase information in quasi-cycles. These oscillations persist in sparsely connected networks, and variation of the network's
connectivity results in variation of the oscillation frequency. A network of such neurons behaves as a stochastic perturbation
of the deterministic Wilson-Cowan equations, and the network undergoes noisy limit cycles or quasi-cycles depending on
whether these have limit cycles or a weakly stable focus. These mechanisms provide a new perspective on the emergence of

  

Source: Andrzejak, Ralph Gregor - Departament de Tecnologia, Universitat Pompeu Fabra

 

Collections: Computer Technologies and Information Sciences