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The purpose of this paper is trifold -- to serve as an instructive resourceand a reference catalog for biologically plausible modeling with i)conductance-based models, coupled with ii) strength-varying slow synapsemodels, culminating in iii) two canonical pair-wise rhythm-generating networks.We document the properties of basic network components: cell models andsynaptic models, which are prerequisites for proper network assembly. Using theslow-fast decomposition we present a detailed analysis of the cellular dynamicsincluding a discussion of the most relevant bifurcations. Several approaches tomodel synaptic coupling are also discussed, and a new logistic model of slowsynapses is introduced. Finally, we describe and examine two types ofbicellular rhythm-generating networks: i) half-center oscillators ii)excitatory-inhibitory pairs and elucidate a key principle -- the networkhysteresis underlying the stable onset of emergent slow bursting in theseneural building blocks. These two cell networks are a basis for morecomplicated neural circuits of rhythmogensis and feature in our models of swimcentral pattern generators.

Pairing cellular and synaptic dynamics into building blocks of rhythmic neural circuits