Synchrony and desynchrony in integrate-and-fire oscillators

Abstract

Due to many experimental reports of synchronous neural activity in the brain, there is much interest in understanding synchronization in networks of neural oscillators and its potential for computing perceptual organization. Contrary to Hopfield and Herz (1995), we find that networks of locally coupled integrate-and-fire oscillators can quickly synchronize. Furthermore, we examine the time needed to synchronize such networks. We observe that these networks synchronize at times proportional to the logarithm of their size, and we give the parameters used to control the rate of synchronization. Inspired by locally excitatory globally inhibitory oscillator network (LEGION) dynamics with relaxation oscillators (Terman & Wang, 1995), we find that global inhibition can play a similar role of desynchronization in a network of integrate-and-fire oscillators. We illustrate that a LEGION architecture with integrate-and-fire oscillators can be similarly used to address image analysis.

New attractor states for synchronous activity in synfire chains with excitatory and inhibitory coupling

“…As it has been shown in various simulations (Gerstner and van Hemmen 1992;Herrmann et al 1995;Pinsky and Rinzel 1995;Arnoldi et al 1996;Hertz and Pru¨gel-Bennett 1996;Marsalek et al 1997;Rudd and Brown 1997;Hansel et al 1998;Kempter et al 1998;Campbell et al 1999;Deco and Schu¨rmann 1999), in a multilayered feedforward neural network, consisting of IFN models, synchronous firing can be achieved in successive layers, even if the feeding input of the network is not synchronized itself.…”

“…Being a relatively close approximation to the biological neuron, the integrate-and-fire neuron (IFN) model is a good choice for studying computational properties of biological neural systems -such as synchrony -by means of simulation (Gerstner and van Hemmen 1992;Niebur and Koch 1994;Herrmann et al 1995;Hopfield and Herz 1995;Arnoldi and Brauer 1996;Horn and Opher 1997;Rudd and Brown 1997;Tal and Schwartz 1997;Hansel et al 1998;Kempter et al 1998;Lin et al 1998;Burkitt and Clark 1999;Campbell et al 1999;Deco and Schu¨rmann 1999).…”

Temporal-to-spatial dynamic mapping, flexible recognition, and temporal correlations in an olfactory cortex model

“…After that, due to the neural fatigue, the winning ensemble stops firing and the second-strongest ensemble wins and fires during the next several cycles (Campbell and Wang 1998;Hoshino et al 1998;Malsburg 1992). To realize such pattern segmentation, the modified network from Sect.…”

“…There are experimental data that suggest that in the brain these tasks are solved with temporal processing (Fujii et al 1996;Jinks and Laing 1999), and there are models that propose possible mechanisms (Ambros-Ingerson et al 1990;Campbell and Wang 1998;Grossberg 1999;Hendin et al 1998;Lysetskiy et al 2001;Malsburg 1992). In Sect.…”

“…An exception is made for the very first input spike in the first cycle, which alone is able to activate the corresponding neuron. This adds to the model the functional property of the networks like the so-called LEGION, where the global inhibition of the neurons depends on the number of the activated neurons (Campbell and Wang 1998). Such inhibition Fig.…”