Combinatorial vector fields on simplicial complexes introduced by Robin Forman constitute
a combinatorial analogue of classical flows. They have found numerous and varied …

This paper discusses a novel approach to obtaining mathematically rigorous results on the
global dynamics of ordinary differential equations. We study switching models of regulatory …

Recurrent versus gradient-like behavior in global dynamics can be characterized via a
surjective lattice homomorphism between certain bounded, distributive lattices, that is …

We construct topological invariants, called abstract weak orbit spaces, of flows and
homeomorphisms on topological spaces. In particular, the abstract weak orbit spaces of …

A new algorithm for computing the Conley index of the Poincaré map of a time-periodic
nonautonomous ordinary differential equation is presented. The algorithm is based on a …

We describe a computational method for constructing a coarse combinatorial model of some
dynamical system in which the macroscopic states are given by elementary cycling motions …

This thesis deals with the numerical computation of the Conley index, an invariant which is
useful for analyzing dynamical systems. It was developed in the 1970s for flows, ie …

We construct topological invariants, called abstract weak orbit spaces, of flows and
homeomorphisms on topological spaces, to describe both gradient dynamics and recurrent …