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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

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
MathSciNet review: 1354959
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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
Email: mischaik@math.gatech.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-96-00207-X
PII: S 0894-0347(96)00207-X
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