The impact of constant effort harvesting on the dynamics of a discrete-time contest competition model

Ziyad Alsharawi*, Amal Amleh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study a general discrete-time model representing the dynamics of a contest competition species with constant effort exploitation. In particular, we consider the difference equation xn+1 = xn f(xn−k) − hxn where h > 0, k ∈ {0, 1}, and the density dependent function f satisfies certain conditions that are typical of a contest competition. The harvesting parameter h is considered as the main parameter, and its effect on the general dynamics of the model is investigated. In the absence of delay in the recruitment (k = 0), we show the effect of h on the stability, the maximum sustainable yield, the persistence of solutions, and how the intraspecific competition change from contest to scramble competition. When the delay in recruitment is 1 (k = 1), we show that a Neimark-Sacker bifurcation occurs, and the obtained invariant curve is supercritical. Furthermore, we give a characterization of the persistent set.

Original languageEnglish
Pages (from-to)6747-6759
Number of pages13
JournalMathematical Methods in the Applied Sciences
Volume40
Issue number18
DOIs
Publication statusPublished - Dec 2017
Externally publishedYes

Keywords

  • Contest competition
  • Neimark-Sacker bifurcation
  • Persistence
  • Scramble competition

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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