On impulsive Beverton-holt difference equations and their applications. (English) Zbl 1068.39005

Berezansky, Leonid; Braverman, Elena

J. Difference Equ. Appl. 10, No. 9, 851-868 (2004).

The authors consider asymptotic properties of the impulsive Beverton-Holt difference equation \[ x_{n+1}=\frac{\alpha _nx_n}{1+B_nx_n},\;x_{pk}^{+}=b_kx_{pk}-d_k,\;n,k=1,2, \ldots , \] where \(p\) is a fixed positive integer. The results obtained are applied to an impulsive logistic equation with non-constant coefficients \[ x^{\prime }(t)=x(t)(r(t)-a(t)x(t)),\;x(\tau _k)=b_kx(\tau _k^{-})-d_k,\;\lim_{k\rightarrow \infty }\tau _k=\infty . \] In particular, sufficient extinction and non-extinction conditions are obtained for both equations.

Reviewer: Wan-Tong Li (Lanzhou)

MSC:

39A11	Stability of difference equations (MSC2000)
34K45	Functional-differential equations with impulses
92B99	Mathematical biology in general
39A20	Multiplicative and other generalized difference equations, e.g., of Lyness type

Keywords:

Beverton-Holt rational difference equation; impulsive harvesting; asymptotic behavior; logistic equation

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