Synchronization of pulse-coupled biological oscillators
SIAM Journal on Applied Mathematics
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Dynamics of functional coupling in the cerebral cortex: an attempt at a model-based interpretation
Proceedings of the NATO advanced research workshop and EGS topical workshop on Chaotic advection, tracer dynamics and turbulent dispersion
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
On numerical simulations of integrate-and-fire neural networks
Neural Computation
Chaotic balanced state in a model of cortical circuits
Neural Computation
Spiking Neuron Models: An Introduction
Spiking Neuron Models: An Introduction
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
High-conductance states in a neuromorphic hardware system
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Cross-correlations in high-conductance states of a model cortical network
Neural Computation
Self-sustained irregular activity in 2-D small-world networks of excitatory and inhibitory neurons
IEEE Transactions on Neural Networks
Journal of Computational Neuroscience
A new method to infer higher-order spike correlations from membrane potentials
Journal of Computational Neuroscience
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We studied the dynamics of large networks of spiking neurons with conductance-based (nonlinear) synapses and compared them to networks with current-based (linear) synapses. For systems with sparse and inhibition-dominated recurrent connectivity, weak external inputs induced asynchronous irregular firing at low rates. Membrane potentials fluctuated a few millivolts below threshold, and membrane conductances were increased by a factor 2 to 5 with respect to the resting state. This combination of parameters characterizes the ongoing spiking activity typically recorded in the cortex in vivo. Many aspects of the asynchronous irregular state in conductance-based networks could be sufficiently well characterized with a simple numerical mean field approach. In particular, it correctly predicted an intriguing property of conductance-based networks that does not appear to be shared by current-based models: they exhibit states of low-rate asynchronous irregular activity that persist for some period of time even in the absence of external inputs and without cortical pacemakers. Simulations of larger networks (up to 350,000 neurons) demonstrated that the survival time of self-sustained activity increases exponentially with network size.