Oscillation analysis of \(\theta\)-methods for the Nicholson's blowflies model
type: Item
instance of: scholarly article
zbMATH Open document ID: 1343.65081
author: Qi Wang
published in: Mathematical Methods in the Applied Sciences
publication date: 2016-04-26T00:00:00Z
Mathematics Subject Classification ID: 65L03
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34K28
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 6574170
zbMATH Keywords: \(\theta\)-method
zbMATH Keywords: oscillation
zbMATH Keywords: numerical example
MaRDI profile type: Publication
full work available at URL: mma.3534
OpenAlex ID: W1945812535
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DOI: 10.1002/MMA.3534
title: Oscillation analysis of \(\theta\)-methods for the Nicholson's blowflies model
review text: The paper is concerned with discretizations of Nicholson's blowflies model NEWLINE\[NEWLINE N'(t)=-\delta N(t)+PN(t-\tau)e^{-aN(t-\tau)},\quad t\geq 0, NEWLINE\]NEWLINE w.r.t. oscillations arround the positive equilibrium NEWLINE\[NEWLINE N^\ast:=\frac{1}{a}\log\frac{P}{\delta}. NEWLINE\]NEWLINE Both for the linear \(\theta\)-method as well as for the one-leg \(\theta\)-method, the author derives various conditions under with the numerical solution oscillates. In addition, it is established that every non-oscillatory discretized solution tends to the equilibrium point \(N^\ast\). These results are illustrated using numerical simulations.
reviewed by: Christian Pötzsche
description: scientific article; zbMATH DE number 6574170