Abstract

There is a growing body of evidence that slow brain rhythms are generated by simple inhibitory neural networks. Sequential switching of tonic spiking activity is a widespread phenomenon underlying such rhythms. A realistic generative model explaining such reproducible switching is a dynamical system that employs a closed stable heteroclinic channel (SHC) in its phase space. Despite strong evidence on the existence of SHC, the conditions on its emergence in a spiking network are unclear. In this paper, we analyze a minimal, reciprocally connected circuit of three spiking units and explore all possible dynamical regimes and transitions between them. We show that the SHC arises due to a Neimark-Sacker bifurcation of an unstable cycle.

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