ON THE GLOBAL DYNAMICS OF ATTRACTORS FOR SCALAR DELAY EQUATIONS

A semi-conjugacy from the dynamics of the global attractors for a fami ly of scalar delay differential equations with negative feedback onto the dynamics of a simple system of ordinary differential equations is constructed. The construction and proof are done in an abstract settin g, and hence, are valid for a variety of dynamical systems which need not arise from delay equations. The proofs are based on the Conley ind ex theory.