a1 Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
a2 Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
Letbe an attractor network for a dynamical system ft: M → M, indexed by the lower sets of a partially ordered set P. Our main theorem asserts the existence of a Lyapunov map ψ:M → K(P) which defines the attractor network. This result is used to prove the existence of connection matrices for discrete-time dynamical systems.
(Received November 27 1990)