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arXiv · 1506.03212

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

Peter Ashwin·Claire Postlethwaite
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Abstract

We give a constructive method for realizing an arbitrary directed graph (with no one-cycles) as a heteroclinic or an excitable dynamic network in the phase space of a system of coupled cells of two types. In each case, the system is expressed as a system of first order differential equations. One of the cell types (the $p$-cells) interacts by mutual inhibition and classifies which vertex (state) we are currently close to, while the other cell type (the $y$-cells) excites the $p$-cells selectively and becomes active only when there is a transition between vertices. We exhibit open sets of parameter values such that these dynamical networks exist and demonstrate via numerical simulation that they can be attractors for suitably chosen parameters.

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Peter Ashwin, Claire Postlethwaite. 2015-06-10. Designing heteroclinic and excitable networks in phase space using two populations of coupled cells. https://doi.org/10.1007/s00332-015-9277-2

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