Cluster synchronization in an ensemble of neurons interacting through chemical synapses

Details Cluster synchronization in an ensemble of neurons interacting through chemical synapses Cluster synchronization in an ensemble of neurons interacting through chemical synapses

2005-04-27

arxiv.org/abs/nlin/0504057v2

Nonlinear Sciences

Pattern Formation and Solitons

Notation for Jacobi matrix is changed. Accepted for publication in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.71.061914

In networks of periodically firing spiking neurons that are interconnected with chemical synapses, we analyze cluster state, where an ensemble of neurons are subdivided into a few clusters, in each of which neurons exhibit perfect synchronization. To clarify stability of cluster state, we decompose linear stability of the solution into two types of stabilities: stability of mean state and stabilities of clusters. Computing Floquet matrices for these stabilities, we clarify the total stability of cluster state for any types of neurons and any strength of interactions even if the size of networks is infinitely large. First, we apply this stability analysis to investigating synchronization in the large ensemble of integrate-and-fire (IF) neurons. In one-cluster state we find the change of stability of a cluster, which elucidates that in-phase synchronization of IF neurons occurs with only inhibitory synapses. Then, we investigate entrainment of two clusters of IF neurons with different excitability. IF neurons with fast decaying synapses show the low entrainment capability, which is explained by a pitchfork bifurcation appearing in two-cluster state with change of synapse decay time constant. Second, we analyze one-cluster state of Hodgkin-Huxley (HH) neurons and discuss the difference in synchronization properties between IF neurons and HH neurons.

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