On the global dynamics of attractors for scalar delay equations

Abstract

A semi-conjugacy from the dynamics of the global attractors for a family of scalar delay differential equations with negative feedback <italic>onto</italic> the dynamics of a simple system of ordinary differential equations is constructed. The construction and proof are done in an abstract setting, and hence, are valid for a variety of dynamical systems which need not arise from delay equations. The proofs are based on the Conley index theory.