Parabolic bursting in an excitable system coupled with a slow oscillation
SIAM Journal on Applied Mathematics
Synchrony in excitatory neural networks
Neural Computation
Weakly connected neural networks
Weakly connected neural networks
Linearization of F-1 curves by adaptation
Neural Computation
Neuronal Networks of the Hippocampus
Neuronal Networks of the Hippocampus
Patterns of Synchrony in Neural Networks with Spike Adaptation
Neural Computation
Type i membranes, phase resetting curves, and synchrony
Neural Computation
IEEE Transactions on Neural Networks
A universal model for spike-frequency adaptation
Neural Computation
The Combined Effects of Inhibitory and Electrical Synapses in Synchrony
Neural Computation
Low-Dimensional Maps Encoding Dynamics in Entorhinal Cortex and Hippocampus
Neural Computation
Study on the role of GABAergic synapses in synchronization
Neurocomputing
Phase-resetting curve determines how BK currents affect neuronal firing
Journal of Computational Neuroscience
Development of a computer algorithm for feedback controlled electrical nerve fiber stimulation
Computer Methods and Programs in Biomedicine
Journal of Computational Neuroscience
Synchronization of delayed coupled neurons in presence of inhomogeneity
Journal of Computational Neuroscience
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There are several different biophysical mechanisms for spike frequency adaptation observed in recordings from cortical neurons. The two most commonly used in modeling studies are a calcium-dependent potassium current Iahp and a slow voltage-dependent potassium current, Im. We show that both of these have strong effects on the synchronization properties of excitatorily coupled neurons. Furthermore, we show that the reasons for these effects are different. We show through an analysis of some standard models, that the M-current adaptation alters the mechanism for repetitive firing, while the afterhyperpolarization adaptation works via shunting the incoming synapses. This latter mechanism applies with a network that has recurrent inhibition. The shunting behavior is captured in a simple two-variable reduced model that arises near certain types of bifurcations. A one-dimensional map is derived from the simplified model.