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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

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Dynamics Analysis and Optimality in Selective Harvesting Predator-Prey Model With Modified Leslie-Gower and Holling-Type II

W. Abid / R. Yafia
  • Corresponding author
  • Ibn Tofail Universit, Faculty of Sciences, Department of Mathematics, Campus Universitaire, BP 133, Kénitra, Morocco
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ M. A. Aziz-Alaoui
  • LMAH, FR-CNRS-3335, Université du Havre Normandie, 25 Rue Ph. Lebon, BP:540, 76058 Le Havre Cedex, (Normandie) France
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  • Other articles by this author:
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/ Ahmed Aghriche
Published Online: 2019-03-22 | DOI: https://doi.org/10.1515/msds-2019-0001


In this work, we consider the optimal harvesting and stability problems of a prey-predator model with modified Leslie-Gower and Holling-type II functional response. The model is governed by a system of three differential equations which describe the interactions between prey, predator and harvesting effort. Boundedness and existence of solutions for this system are showed. The existence and local stability of the possible steady states are analyzed and the conditions of global stability of the interior equilibrium are established by using the Lyapunov function, we prove also the occurrence of Hopf bifurcation at this point. By using the Pontryagin’s maximal principle, we formulate and we solve the problem of the optimal harvest policy. In the end, some numerical simulations are given to support our theoretical results.

Keywords: Predator-prey model; ordinary differential equations; local and global stability; bifurcation; optimal harvesting policy


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About the article

Received: 2018-04-02

Accepted: 2019-02-25

Published Online: 2019-03-22

Published in Print: 2019-03-01

Citation Information: Nonautonomous Dynamical Systems, Volume 6, Issue 1, Pages 1–17, ISSN (Online) 2353-0626, DOI: https://doi.org/10.1515/msds-2019-0001.

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© 2019 W. Abid et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 Public License. BY 4.0

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