Designing computational systems using heteroclinic networks

Peter Ashwin
College of Engineering, Mathematics and Physical Sciences, University of Exeter

(March 27, 2013 3:00 PM - 3:50 PM)

Designing computational systems using heteroclinic networks

Abstract

In this talk I will present some methods for constructing coupled dynamical systems out of simple bistable units that allow one to realise arbitrary finite state computational systems using coupled ordinary differential equations. More precisely, suppose one has an arbitrary strongly connected finite directed graph. How does one construct a systems of coupled cells that realises this graphs as attracting heteroclinic networks, with minimal limitations? The constructions are robust with respect to a suitably constrained set of perturbations and to addition of noise. On the presence of noise, there may or may not be short-term memory effects associated with the previous path on the network. This is joint work with C. Postlethwaite (Auckland).