Phase-locking in weakly heterogeneous neuronal networks

Details Phase-locking in weakly heterogeneous neuronal networks Phase-locking in weakly heterogeneous neuronal networks

1997-09-19

arxiv.org/abs/cond-mat/9709220v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

RevTex, 27 pages, 3 figures

Scientific paper

10.1016/S0167-2789(98)00082-7

We examine analytically the existence and stability of phase-locked states in a weakly heterogeneous neuronal network. We consider a model of N neurons with all-to-all synaptic coupling where the heterogeneity is in the firing frequency or intrinsic drive of the neurons. We consider both inhibitory and excitatory coupling. We derive the conditions under which stable phase-locking is possible. In homogeneous networks, many different periodic phase-locked states are possible. Their stability depends on the dynamics of the neuron and the coupling. For weak heterogeneity, the phase-locked states are perturbed from the homogeneous states and can remain stable if their homogeneous conterparts are stable. For enough heterogeneity, phase-locked solutions either lose stability or are destroyed completely. We analyze the possible states the network can take when phase-locking is broken.

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