On impulsive beverton-holt difference equations and their applications

Leonid Berezansky; Elena Braverman

doi:10.1080/10236190410001726421

On impulsive beverton-holt difference equations and their applications

Leonid Berezansky, Elena Braverman

Department of Mathematics

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

87 Scopus citations

Abstract

The asymptotic properties of the impulsive Beverton-Holt difference equation X_n+1 = α_nx_n/1 + B _nx_n X_pk⁺ = b_kX _pk - d_k, n,k = 1,2,..., where p is a fixed positive integer, are considered. The results are applied to an impulsive logistic equation with non-constant coefficients ẋ(t) = x(t)(r(t) - a(t)x(t)), x(τ_k) = b_kx(τ_k^-) - d _k, limτ_kk→∞ = ∞ In particular, sufficient extinction and non-extinction conditions are obtained for both equations.

Original language	English
Pages (from-to)	851-868
Number of pages	18
Journal	Journal of Difference Equations and Applications
Volume	10
Issue number	9
DOIs	https://doi.org/10.1080/10236190410001726421
State	Published - 10 Aug 2004

Keywords

Asymptotic behavior
Beverton-Holt difference equation
Impulsive harvesting
Logistic equations

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

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10.1080/10236190410001726421

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title = "On impulsive beverton-holt difference equations and their applications",

abstract = "The asymptotic properties of the impulsive Beverton-Holt difference equation Xn+1 = αnxn/1 + B nxn Xpk+ = bkX pk - dk, n,k = 1,2,..., where p is a fixed positive integer, are considered. The results are applied to an impulsive logistic equation with non-constant coefficients ẋ(t) = x(t)(r(t) - a(t)x(t)), x(τk) = bkx(τk-) - d k, limτkk→∞ = ∞ In particular, sufficient extinction and non-extinction conditions are obtained for both equations.",

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AU - Braverman, Elena

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N2 - The asymptotic properties of the impulsive Beverton-Holt difference equation Xn+1 = αnxn/1 + B nxn Xpk+ = bkX pk - dk, n,k = 1,2,..., where p is a fixed positive integer, are considered. The results are applied to an impulsive logistic equation with non-constant coefficients ẋ(t) = x(t)(r(t) - a(t)x(t)), x(τk) = bkx(τk-) - d k, limτkk→∞ = ∞ In particular, sufficient extinction and non-extinction conditions are obtained for both equations.

AB - The asymptotic properties of the impulsive Beverton-Holt difference equation Xn+1 = αnxn/1 + B nxn Xpk+ = bkX pk - dk, n,k = 1,2,..., where p is a fixed positive integer, are considered. The results are applied to an impulsive logistic equation with non-constant coefficients ẋ(t) = x(t)(r(t) - a(t)x(t)), x(τk) = bkx(τk-) - d k, limτkk→∞ = ∞ In particular, sufficient extinction and non-extinction conditions are obtained for both equations.

KW - Asymptotic behavior

KW - Beverton-Holt difference equation

KW - Impulsive harvesting

KW - Logistic equations

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ER -

On impulsive beverton-holt difference equations and their applications

Abstract

Keywords

ASJC Scopus subject areas

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