Analysis of neural excitability and oscillations
Methods in neuronal modeling
Synchronization of pulse-coupled biological oscillators
SIAM Journal on Applied Mathematics
Synchrony in excitatory neural networks
Neural Computation
The influence of limit cycle topology on the phase resetting curve
Neural Computation
Low-Dimensional Maps Encoding Dynamics in Entorhinal Cortex and Hippocampus
Neural Computation
Type i membranes, phase resetting curves, and synchrony
Neural Computation
Hi-index | 0.00 |
Phase response curves (PRCs) have been widely used to study synchronization in neural circuits comprised of pacemaking neurons. They describe how the timing of the next spike in a given spontaneously firing neuron is affected by the phase at which an input from another neuron is received. Here we study two reciprocally coupled clusters of pulse coupled oscillatory neurons. The neurons within each cluster are presumed to be identical and identically pulse coupled, but not necessarily identical to those in the other cluster. We investigate a two cluster solution in which all oscillators are synchronized within each cluster, but in which the two clusters are phase locked at nonzero phase with each other. Intuitively, one might expect this solution to be stable only when synchrony within each isolated cluster is stable, but this is not the case. We prove rigorously the stability of the two cluster solution and show how reciprocal coupling can stabilize synchrony within clusters that cannot synchronize in isolation. These stability results for the two cluster solution suggest a mechanism by which reciprocal coupling between brain regions can induce local synchronization via the network feedback loop.