MUTUALLY PULSE-COUPLED NEURONS THAT DO NOT SYNCHRONIZE IN ISOLATION CAN SYNCHRONIZE VIA RECIPROCAL COUPLING WITH ANOTHER NEURAL POPULATION
Document Type
Presentation
Start Date
22-10-2010 3:00 PM
End Date
22-10-2010 4:30 PM
Description
We examine two reciprocally coupled clusters of pulse-coupled oscillatory neurons. Neurons within each cluster are presumed to be identical and identically coupled but not necessarily identical to neurons in the other cluster. We construct a discrete map using Phase Response Curves (PRCs) for a firing pattern in which the neurons within each cluster are synchronized but the two clusters fire out of phase with respect to each other. We extend this map to include a perturbation of a single neuron within one cluster and linearize about the fixed point of the original map. We derive expressions that give stability of the phase-locked cluster solution using only the slopes of the PRC at the locking points. We give an example of a cluster of inhibitory Type II excitable neurons that cannot synchronize in isolation because the absolute value of the eigenvalue that determines synchrony in the isolated cluster is greater than one. The reciprocal coupling with another cluster scales this eigenvalue such that it becomes less than one, thus guaranteeing stability. These results suggest a mechanism by which local synchronization can be induced through reciprocal coupling between brain regions via the feedback loop.
Recommended Citation
Chandrasekaran, Lakshmi; Acthuthan, S.; and Canavier, C. C., "MUTUALLY PULSE-COUPLED NEURONS THAT DO NOT SYNCHRONIZE IN ISOLATION CAN SYNCHRONIZE VIA RECIPROCAL COUPLING WITH ANOTHER NEURAL POPULATION" (2010). Dr. Joseph M. Moerschbaecher, III Graduate Research Day. 5.
https://digitalscholar.lsuhsc.edu/grad_rs/2010/poster2/5
MUTUALLY PULSE-COUPLED NEURONS THAT DO NOT SYNCHRONIZE IN ISOLATION CAN SYNCHRONIZE VIA RECIPROCAL COUPLING WITH ANOTHER NEURAL POPULATION
We examine two reciprocally coupled clusters of pulse-coupled oscillatory neurons. Neurons within each cluster are presumed to be identical and identically coupled but not necessarily identical to neurons in the other cluster. We construct a discrete map using Phase Response Curves (PRCs) for a firing pattern in which the neurons within each cluster are synchronized but the two clusters fire out of phase with respect to each other. We extend this map to include a perturbation of a single neuron within one cluster and linearize about the fixed point of the original map. We derive expressions that give stability of the phase-locked cluster solution using only the slopes of the PRC at the locking points. We give an example of a cluster of inhibitory Type II excitable neurons that cannot synchronize in isolation because the absolute value of the eigenvalue that determines synchrony in the isolated cluster is greater than one. The reciprocal coupling with another cluster scales this eigenvalue such that it becomes less than one, thus guaranteeing stability. These results suggest a mechanism by which local synchronization can be induced through reciprocal coupling between brain regions via the feedback loop.
Comments
See abstract book page 49