# PFD

## Seminar

### Linear and ODE-equivalence for coupled cell networks

Dias, A (Porto)
Tuesday 27 September 2005, 17:00-17:30

Seminar Room 1, Newton Institute

#### Abstract

Coupled cell systems are systems of ODEs, defined by admissible' vector fields, associated with a network whose nodes represent variables and whose edges specify couplings between nodes. It is known that non-isomorphic networks can correspond to the same space of admissible vector fields. Such networks are said to be ODE-equivalent'. We prove that two networks are ODE-equivalent if and only if they determine the same space of linear vector fields; moreover, the variable associated with each node may be assumed 1-dimensional for that purpose.

This is a joint work with Ian Stewart (Warwick, UK)