Journal of Nonlinear Science

, Volume 26, Issue 2, pp 345–364 | Cite as

Designing Heteroclinic and Excitable Networks in Phase Space Using Two Populations of Coupled Cells



We give a constructive method for realising 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.


Heteroclinic network Excitable network Coupled dynamical system 

Mathematics Subject Classification

37C80 34C37 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Center for Systems, Dynamics and Control, Department of MathematicsUniversity of ExeterExeterUK
  2. 2.Department of MathematicsUniversity of AucklandAucklandNew Zealand

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