40-Hz coherent oscillations in neuronal systems

A characteristic coherent oscillation with a frequency of 40 Hz which relates to some functions of the brain is shown to be intrinsic due to the nonlinear firing of spikes of neurons when the network is situated in a stimulus-induced oscillatory state. This oscillation mode is associated with a synchronized firing pattern, and is robust to a variety of couplings between the neurons and to a wide range of external stimuli. @S1063-651X~97!05409-3# PACS number~s!: 87.10.1e Recently, considerable attention has been drawn to the existence of coherent synchronized oscillatory activity in many neuronal systems. It has been found experimentally that large-scale synchronized neuronal activity is often accompanied by oscillatory firing patterns with a frequency about 40 Hz ~in the g band, usually referred to as 40-Hz oscillations !@ 1 #. For example, in the cat’s visual cortex and in the awake ~or in rapid-eye-movement sleep! state of humans, coherent synchronized oscillatory responses have been observed through local field potential and multiunit activities @1#. It has also been shown that the synchronization probability depends on the configuration of visual stimuli and that it does reflect some of the gestalt criteria that are used for scene segmentation @1#. Therefore this kind of long-distance synchronized spatiotemporal dynamical behavior has been suggested as a mechanism for the binding of spatially distributed features into a coherent object @1‐3#. The neurons which process different features of the same object oscillate with a fixed phase, while neurons which code different objects oscillate with different phases or at random. To date, there have been some theoretical studies on the above mentioned coherent oscillations; these are based either on a model of coupled oscillators or a model of integrate and fire; few of them have taken into account the detailed features of the neuronal activity, such as its recovery or its adaptation after the firing of spikes. Although a completely synchronized oscillation with zero phase difference may be obtained in these models, all the couplings are assumed to be excitatory @4#, an assumption which seems to be oversimplified and which may not be consistent with the real situation. In particular, the biophysical origin of these coherent oscillations and their relationship with the synaptic interaction ~or coupling!, as well as with the external stimuli, are not well studied. In addition, the frequency spectrum of the oscillations has rarely been addressed theoretically, and the question of how the synchrony is established and what role the oscillatory firing plays in the dynamical informational pro