JournalszaaVol. 21, No. 4pp. 1015–1025

Existence and Asymptotic Behavior of Positive Solutions of a Non-Autonomous Food-Limited Model with Unbounded Delay

  • Yuji Liu

    Beijing Institute of Technology, China
  • Weigao Ge

    Beijing Institute of Technology, China
Existence and Asymptotic Behavior of Positive Solutions of a Non-Autonomous Food-Limited Model with Unbounded Delay cover
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Abstract

Consider the non-autonomous logistic model

Δxn=pnxn1xnkn1+λxnknr      (n0)\Delta x_n = p_n x_n \frac{1–x_n–k_n}{1+\lambda x_n–k_n}^r \;\;\;(n≥0)

where Δxn=xn+1xn\Delta x_n = x-{n+1} – x_n, {pnp_n} is a sequence of positive real numbers, {knk_n} is a sequence of non-negative integers such that {nknn–k_n} is non-decreasing, λ[0,1]\lambda \in [0,1], and rr is the ratio of two odd integers. We obtain new sufficient conditions for the attractivity of the equilibrium x=1x = 1 of the model and conditions that guarantee the solution to be positive, which improve and generalize some recent results established by Phios and by Zhou and Zhang.

Cite this article

Yuji Liu, Weigao Ge, Existence and Asymptotic Behavior of Positive Solutions of a Non-Autonomous Food-Limited Model with Unbounded Delay. Z. Anal. Anwend. 21 (2002), no. 4, pp. 1015–1025

DOI 10.4171/ZAA/1123