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
Weakly connected neural networks
Weakly connected neural networks
Chaotic balanced state in a model of cortical circuits
Neural Computation
Patterns of Synchrony in Neural Networks with Spike Adaptation
Neural Computation
Synchronization of the Neural Response to Noisy Periodic Synaptic Input
Neural Computation
Type i membranes, phase resetting curves, and synchrony
Neural Computation
IEEE Transactions on Neural Networks
Stimulus Competition by Inhibitory Interference
Neural Computation
Low-Dimensional Maps Encoding Dynamics in Entorhinal Cortex and Hippocampus
Neural Computation
Awaking and sleeping of a complex network
Neural Networks
Spike-timing error backpropagation in theta neuron networks
Neural Computation
Adaptive synchronization of activities in a recurrent network
Neural Computation
Stability of two cluster solutions in pulse coupled networks of neural oscillators
Journal of Computational Neuroscience
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part I
Dependence of correlated firing on strength of inhibitory feedback
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part I
Journal of Computational Neuroscience
Journal of Computational Neuroscience
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In model networks of E-cells and I-cells (excitatory and inhibitory neurons, respectively), synchronous rhythmic spiking often comes about from the interplay between the two cell groups: the E-cells synchronize the I-cells and vice versa. Under ideal conditions--homogeneity in relevant network parameters and all-to-all connectivity, for instance--this mechanism can yield perfect synchronization. We find that approximate, imperfect synchronization is possible even with very sparse, random connectivity. The crucial quantity is the expected number of inputs per cell. As long as it is large enough (more precisely, as long as the variance of the total number of synaptic inputs per cell is small enough), tight synchronization is possible. The desynchronizing effect of random connectivity can be reduced by strengthening the E → I synapses. More surprising, it cannot be reduced by strengthening the I → E synapses. However, the decay time constant of inhibition plays an important role. Faster decay yields tighter synchrony. In particular, in models in which the inhibitory synapses are assumed to be instantaneous, the effects of sparse, random connectivity cannot be seen.