Stability of two cluster solutions in pulse coupled networks of neural oscillators |
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Authors: | Lakshmi Chandrasekaran Srisairam Achuthan Carmen C Canavier |
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Institution: | (1) Neuroscience Center of Excellence, LSU Health Sciences Center, New Orleans, LA 70112, USA;(2) Department of Ophthalmology, LSU Health Sciences Center, New Orleans, LA 70112, USA |
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Abstract: | 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. |
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