On the global dynamics of attractors for scalar delay equations

Authors:
Christopher McCord and Konstantin Mischaikow

Journal:
J. Amer. Math. Soc. **9** (1996), 1095-1133

MSC (1991):
Primary 58F12, 58F32, 34K05

DOI:
https://doi.org/10.1090/S0894-0347-96-00207-X

MathSciNet review:
1354959

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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.

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Additional Information

**Christopher McCord**

Affiliation:
Institute for Dynamics University of Cincinnati Cincinnati, Ohio 45221-0025

Email:
chris.mccord@uc.edu

**Konstantin Mischaikow**

Affiliation:
Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, Georgia 30332

MR Author ID:
249919

Email:
mischaik@math.gatech.edu

Received by editor(s):
July 24, 1992

Received by editor(s) in revised form:
September 5, 1995

Additional Notes:
Research was supported in part by NSF Grant DMS-9101412.

Article copyright:
© Copyright 1996
American Mathematical Society