The effect of state dependent delay and harvesting on a stage-structured predator–prey model

Jafar Fawzi M. Al-Omari

Applied Mathematics and Computation, 2015, vol. 271, issue C, 142-153

Abstract: We propose and analyze a stage-structured predator–prey model in which the time from birth to maturity is directly related to the number of individuals present. Individuals mature more quickly when there are fewer of them around. The state dependent time delay is taken to be an increasing differentiable bounded function. In this research, we study the dynamics of our model analytically. We present results on positivity and boundedness of all populations. Criteria for the existence of all equilibria and uniqueness of a positive equilibrium are given. In order to observe the effect of state-dependent maturation delay, local stability analysis around all equilibria of the proposed model is discussed due to variation of maturation delay. Also, global stability of trivial and the boundary equilibria is investigated, using Liapunov functional and LaSalle invariant principle. To investigate the effect of state-dependent maturation delay and the harvesting effort of all species we carried out numerical simulations.

Keywords: Stage structure; Global stability; State-dependent; Harvesting; Predator–prey (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630031501200X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:271:y:2015:i:c:p:142-153

DOI: 10.1016/j.amc.2015.08.119

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().