Dynamics of neural populations: stability and synchrony

Network : Computation in Neural Systems
Lawrence SirovichKip Lubliner

Abstract

A population formulation of neuronal activity is employed to study an excitatory network of (spiking) neurons receiving external input as well as recurrent feedback. At relatively low levels of feedback, the network exhibits time stationary asynchronous behavior. A stability analysis of this time stationary state leads to an analytical criterion for the critical gain at which time asynchronous behavior becomes unstable. At instability the dynamics can undergo a supercritical Hopf bifurcation and the population passes to a synchronous state. Under different conditions it can pass to synchrony through a subcritical Hopf bifurcation. And at high gain a network can reach a runaway state, in finite time, after which the network no longer supports bounded solutions. The introduction of time delayed feedback leads to a rich range of phenomena. For example, for a given external input, increasing gain produces transition from asynchrony, to synchrony, to asynchrony and finally can lead to divergence. Time delay is also shown to strongly mollify the amplitude of synchronous oscillations. Perhaps, of general importance, is the result that synchronous behavior can exist only for a narrow range of time delays, which range is an order of mag...Continue Reading

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Citations

Jun 21, 2012·Journal of Mathematical Biology·Grégory Dumont, Jacques Henry
Nov 7, 2008·Journal of Computational Neuroscience·Chin-Yueh Liu, Duane Q Nykamp
Feb 23, 2013·Journal of Computational Neuroscience·Wilten Nicola, Sue Ann Campbell
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