83 citations · 99 across the 4 of their papers we have counts for
4 papers
New dynamics in cerebellar Purkinje cells: torus canards
M. A. Kramer, R. D. Traub, N. J. Kopell
We describe a transition from bursting to rapid spiking in a reduced mathematical model of a cerebellar Purkinje cell. We perform a slow-fast analysis of the system and find that -…
Frequency control in synchronized networks of inhibitory neurons
Carson C. Chow, John A. White, Jason Ritt +1
We analyze the control of frequency for a synchronized inhibitory neuronal network. The analysis is done for a reduced membrane model with a biophysically-based synaptic influence.…
Synchronization and oscillatory dynamics in heterogeneous mutually inhibited neurons
J. A. White, C. C. Chow, J. Ritt +2
We study some mechanisms responsible for synchronous oscillations and loss of synchrony at physiologically relevant frequencies (10-200 Hz) in a network of heterogeneous inhibitory…
Rhythms of the nervous system: mathematical themes and variations
Nancy Kopell
The nervous system displays a variety of rhythms in both waking and sleep. These rhythms have been closely associated with different behavioral and cognitive states, but it is stil…