Parabolic bursting in an excitable system coupled with a slow oscillation
SIAM Journal on Applied Mathematics
Analysis of neural excitability and oscillations
Methods in neuronal modeling
Synchronization of pulse-coupled biological oscillators
SIAM Journal on Applied Mathematics
Alternating and synchronous rhythms in reciprocally inhibitory model neurons
Neural Computation
Synchrony in excitatory neural networks
Neural Computation
Weakly connected neural networks
Weakly connected neural networks
Patterns of Synchrony in Neural Networks with Spike Adaptation
Neural Computation
Synchrony in Heterogeneous Networks of Spiking Neurons
Neural Computation
Type i membranes, phase resetting curves, and synchrony
Neural Computation
Scaling effects in a model of the olfactory bulb
Neurocomputing
Gamma oscillations and stimulus selection
Neural Computation
Model this! seven empirical phenomena missing in the models of cortical oscillatory dynamics
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Synaptic information transfer in computer models of neocortical columns
Journal of Computational Neuroscience
Journal of Computational Neuroscience
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Synchronous rhythmic spiking in neuronal networks can be brought about by the interaction between E-cells and Icells (excitatory and inhibitory cells). The I-cells gate and synchronize the E-cells, and the E-cells drive and synchronize the I-cells. We refer to rhythms generated in this way as PING (pyramidal-interneuronal gamma) rhythms. The PING mechanism requires that the drive II to the I-cells be sufficiently low; the rhythm is lost when II gets too large. This can happen in at least two ways. In the first mechanism, the I-cells spike in synchrony, but get ahead of the E-cells, spiking without being prompted by the E-cells. We call this phase walkthrough of the I-cells. In the second mechanism, the I-cells fail to synchronize, and their activity leads to complete suppression of the E-cells. Noisy spiking in the E-cells, generated by noisy external drive, adds excitatory drive to the I-cells and may lead to phase walkthrough. Noisy spiking in the I-cells adds inhibition to the E-cells and may lead to suppression of the E-cells. An analysis of the conditions under which noise leads to phase walkthrough of the I-cells or suppression of the E-cells shows that PING rhythms at frequencies far below the gamma range are robust to noise only if network parameter values are tuned very carefully. Together with an argument explaining why the PING mechanism does not work far above the gamma range in the presence of heterogeneity, this justifies the "G" in "PING."