On the discretization of a delay differential equation

Kenneth L. Cooke; Anatoli F. Ivanov

doi:10.1080/10236190008808216

On the discretization of a delay differential equation

Kenneth L. Cooke, Anatoli F. Ivanov

Penn State Wilkes-Barre

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

The dynamics of the delay difference equation μ[Δx_n + αΔx_n-N] = -x_n+1 + f(x_n-N) as n → ∞ is studied for small positive μ. The equation is shown to possess stable periodic solutions that correspond to hyperbolic attracting cycles of the one-dimensional map f.

Original language	English (US)
Pages (from-to)	105-119
Number of pages	15
Journal	Journal of Difference Equations and Applications
Volume	6
Issue number	1
DOIs	https://doi.org/10.1080/10236190008808216
State	Published - 2000

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Applied Mathematics

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10.1080/10236190008808216

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abstract = "The dynamics of the delay difference equation μ[Δxn + αΔxn-N] = -xn+1 + f(xn-N) as n → ∞ is studied for small positive μ. The equation is shown to possess stable periodic solutions that correspond to hyperbolic attracting cycles of the one-dimensional map f.",

author = "Cooke, {Kenneth L.} and Ivanov, {Anatoli F.}",

note = "Funding Information: The authors thank an anonymous referee for sever81 helpful suggestions. This research has bee:: supported by NSF Grant DMS 9502922 (USA) and in part by the Australian Research Council (Australia).",

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N2 - The dynamics of the delay difference equation μ[Δxn + αΔxn-N] = -xn+1 + f(xn-N) as n → ∞ is studied for small positive μ. The equation is shown to possess stable periodic solutions that correspond to hyperbolic attracting cycles of the one-dimensional map f.

AB - The dynamics of the delay difference equation μ[Δxn + αΔxn-N] = -xn+1 + f(xn-N) as n → ∞ is studied for small positive μ. The equation is shown to possess stable periodic solutions that correspond to hyperbolic attracting cycles of the one-dimensional map f.

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On the discretization of a delay differential equation

Abstract

All Science Journal Classification (ASJC) codes

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