Dynamics of delay-coupled adaptive spiking neurons
A prominent feature of many types of neurons is spike frequency adaptation, shown by a decrease in spike rate during prolonged stimulation. This behavior is typically mediated by slow transmembrane potassium currents that can be controlled by neuromodulators . Here we study how such adaptation currents affect the dynamics of coupled neurons in two different regimes, oscillatory and irregular spiking. We analyze synchrony of pairs and networks of coupled oscillating neurons by applying a phase reduction  and master stability function  techniques to the experimentally verified adaptive exponential integrate-and-fire neuron model , taking into account synaptic delays. To characterize the activity of large networks of sparsely connected neurons subject to noisy inputs, we use the same neuron model and a mean-field approach based on the Fokker-Planck equation . For oscillating excitatory neurons we show that adaptation currents can stabilize network synchrony, as long as delays are negligible. In the noisy, irregular spiking regime on the other hand, adaptation modulates neuronal spiking variability and can mediate population bursts.
 D.V. Madison, B. Lancaster, and R.A. Nicoll, Voltage clamp
analysis of cholinergic action in the hippocampus, J. Neurosci. 1987
 J. Ladenbauer, M. Augustin, L. Shiau, and K. Obermayer, Impact of adaptation currents on synchronization of coupled exponential integrate-and-fire neurons, PLoS Comput. Biol. 2012
 L.M. Pecora and T.L. Carroll, Master stability functions for synchronized coupled systems, PRL 1998
 R. Brette and W. Gerstner, Adaptive exponential integrate-and-fire model as an effective description of neuronal activity, J. Neurophysiol. 2005
 N. Brunel, Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons, J. Comput. Neurosci. 2000