Dynamics of a predator–prey model with harvesting and reserve area for prey in the presence of competition and toxicity

The aim of this paper is to present and study a three-dimensional continuous time dynamical system modeling a predator–prey with harvesting and reserve zone for the prey in the presence of competition and toxicity. We first prove that our model is ecologically and mathematically well-posed. In addit...

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Bibliographic Details
Published in:Journal of applied mathematics & computing 2019-02, Vol.59 (1-2), p.305-321
Main Authors: Louartassi, Younes, Alla, Abdellah, Hattaf, Khalid, Nabil, Aissam
Format: Article
Language:English
Subjects:
Applied mathematics
Competition
Computational Mathematics and Numerical Analysis
Computer simulation
Continuous time systems
Ecological monitoring
Economic models
Harvesting
Mathematical and Computational Engineering
Mathematical models
Mathematics
Mathematics and Statistics
Mathematics of Computing
Maximum principle
Original Research
Predator-prey simulation
Stability analysis
Theory of Computation
Three dimensional models
Toxicity
Well posed problems
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Summary:The aim of this paper is to present and study a three-dimensional continuous time dynamical system modeling a predator–prey with harvesting and reserve zone for the prey in the presence of competition and toxicity. We first prove that our model is ecologically and mathematically well-posed. In addition, the stability analysis is investigated by direct and indirect Lyapunov methods. By using the Pontryagin’s maximum principle, an optimal harvesting policy is established. Furthermore, numerical simulations are given in order to illustrate our theoretical results.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-018-1181-0