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On the global dynamics of attractors for scalar delay equations. (English) Zbl 0861.58023

Summary: A semi-conjugacy from the dynamics of the global attractors for a family 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 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.

MSC:

37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37B30 Index theory for dynamical systems, Morse-Conley indices
37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems
34K05 General theory of functional-differential equations
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