We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Designing Heteroclinic and Excitable Networks in Phase Space Using Two Populations of Coupled Cells.
- Authors
Ashwin, Peter; Postlethwaite, Claire
- Abstract
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.
- Subjects
PHASE space; DYNAMICAL systems; MATHEMATICAL decoupling; GEOMETRIC vertices; ATTRACTORS (Mathematics); COMPUTER simulation; DIFFERENTIAL equations
- Publication
Journal of Nonlinear Science, 2016, Vol 26, Issue 2, p345
- ISSN
0938-8974
- Publication type
Article
- DOI
10.1007/s00332-015-9277-2