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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

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Volume 19, Issue 3-4

Issues

Analysis of a Delayed Predator–Prey System with Harvesting

Wei Liu
  • School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
  • School of Mathematics and Computer Science, Xinyu University, Xinyu 338004, China
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/ Yaolin Jiang
Published Online: 2018-05-11 | DOI: https://doi.org/10.1515/ijnsns-2017-0094

Abstract

This article is concerned with a Leslie–Gower predator–prey system with the predator being harvested and the prey having a delay due to the gestation of prey species. By regarding the gestation delay as a bifurcation parameter, we first derive some sufficient conditions on the stability of positive equilibrium point and the existence of Hopf bifurcations basing on the local parametrization method for differential-algebra system. In succession, we also investigate the direction of Hopf bifurcations and the stability of bifurcating periodic solutions on the center manifold by employing the center manifold reduction for functional differential equations. Finally, to verify our theoretical predictions, several numerical simulations are given.

Keywords: Leslie-Gower; gestation delay; bifurcation; asymptotically stable; harvest

PACS: 87.10.Ed; 05.45.-a; 87.23.Cc

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About the article

Received: 2017-04-24

Accepted: 2018-01-30

Published Online: 2018-05-11

Published in Print: 2018-06-26


This work is supported by the National Natural Science Foundations of China (Grants No. 11371287 and 61663043), Science and Technology Projects Founded by the Education Department of Jiangxi Province (Grants no. GJJ14774 and GJJ14775).


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 3-4, Pages 335–349, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2017-0094.

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