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We give a constructive method for realizing an arbitrary directed graph (withno one-cycles) as a heteroclinic or an excitable dynamic network in the phasespace of a system of coupled cells of two types. In each case, the system isexpressed as a system of first order differential equations. One of the celltypes (the $p$-cells) interacts by mutual inhibition and classifies whichvertex (state) we are currently close to, while the other cell type (the$y$-cells) excites the $p$-cells selectively and becomes active only when thereis a transition between vertices. We exhibit open sets of parameter values suchthat these dynamical networks exist and demonstrate via numerical simulationthat they can be attractors for suitably chosen parameters.

Designing heteroclinic and excitable networks in phase space using two populations of coupled cells