Dynamics of Coupled Oscillator Systems - Abstract

Ronge, Robert

Clustering in systems of repulsively coupled Morris--Lecar neurons

We study systems of identical Morris-Lecar neurons with repulsive all-to-all coupling. System parameters are chosen such that for the decoupled case each neuron is at rest, giving rise to a stable synchronous fixed point, but close to a saddle-node on invariant circle bifurcation, a scenario that is known in neurscience as class I excitability. We find that for sufficiently repulsive coupling strength the neurons form in general two or three clusters of spiking neurons of approximately equal size. However, for suitable initial conditions the system may split in three groups, two small spiking clusters in anti-phase and one large cluster of nearly resting neurons whose activity is apparently suppressed by the smaller clusters. Additionally, for coupling strengths close to the bifurcation of the synchronous fixed point we find a transient outlier dynamics in which all neurons for some time spike one after another in a regular fashion before forming two or three large clusters. We investigate how this transient behavior can be related to apparently stable dynamics of the same kind for an active rotator model which obeys Watanabe-Strogatz theory.