Designing heteroclinic and excitable networks in phase space using two populations of coupled cells
Adaptation and Self-Organizing Systems
2015-12-17 v2
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 -cells) interacts by mutual inhibition and classifies which vertex (state) we are currently close to, while the other cell type (the -cells) excites the -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.
Keywords
Cite
@article{arxiv.1506.03212,
title = {Designing heteroclinic and excitable networks in phase space using two populations of coupled cells},
author = {Peter Ashwin and Claire Postlethwaite},
journal= {arXiv preprint arXiv:1506.03212},
year = {2015}
}