Synchronization of pulse-coupled biological oscillators
SIAM Journal on Applied Mathematics
Oscillations and synchronization in neural networks: an exploration of the labeling
International Journal of Neural Systems
Alternating and synchronous rhythms in reciprocally inhibitory model neurons
Neural Computation
Reduction of conductance-based neuron models
Biological Cybernetics
Reduction of conductance-based models with slow synapses to neural nets
Neural Computation
Synchrony in excitatory neural networks
Neural Computation
What matters in neuronal locking?
Neural Computation
Oscillatory and bursting properties of neurons
The handbook of brain theory and neural networks
Spikes: exploring the neural code
Spikes: exploring the neural code
Spatiotemporal spike-encoding of a continuous external signal
Neural Computation
Ergodicity of spike trains: when does trial averaging make sense?
Neural Computation
Response Variability in Balanced Cortical Networks
Neural Computation
On Synchrony of Weakly Coupled Neurons at Low Firing Rate
Neural Computation
Dynamics of Spiking Neurons with Electrical Coupling
Neural Computation
A synchronization metric for meshed networks of pulse-coupled oscillators
Proceedings of the 3rd International Conference on Bio-Inspired Models of Network, Information and Computing Sytems
Synchrony State Generation in Artificial Neural Networks with Stochastic Synapses
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part I
Journal of Computational Neuroscience
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We present a dynamical theory of integrate-and-fire neurons with strong synaptic coupling. We show how phase-locked states that are stable in the weak coupling regime can destabilize as the coupling is increased, leading to states characterized by spatiotemporal variations in the interspike intervals (ISIs). The dynamics is compared with that of a corresponding network of analog neurons in which the outputs of the neurons are taken to be mean firing rates. A fundamental result is that for slow interactions, there is good agreement between the two models (on an appropriately defined timescale). Various examples of desynchronization in the strong coupling regime are presented. First, a globally coupled network of identical neurons with strong inhibitory coupling is shown to exhibit oscillator death in which some of the neurons suppress the activity of others. However, the stability of the synchronous state persists for very large networks and fast synapses. Second, an asymmetric network with a mixture of excitation and inhibition is shown to exhibit periodic bursting patterns. Finally, a one-dimensional network of neurons with long-range interactions is shown to desynchronize to a state with a spatially periodic pattern of mean firing rates across the network. This is modulated by deterministic fluctuations of the instantaneous firing rate whose size is an increasing function of the speed of synaptic response.