EFFECT OF HARVESTING ON A THREE-SPECIES PREDATOR–PREY INTERACTION WITH FRACTIONAL DERIVATIVE

Boukabcha Brahim (), Abdelkader Benali (), Ali Hakem (), Salih Djilali, Anwar Zeb () and Zareen A. Khan
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Boukabcha Brahim: Laboratory ACEDP, Department of Mathematics, Djillali Liabes University, Sidi Bel Abbès 22000, Algeria
Abdelkader Benali: Laboratory LMA, Mathematics Department, Faculty of the Exact Sciences and Computer, University of Hassiba Benbouali, Chlef 02000, Algeria
Ali Hakem: Laboratory ACEDP, Department of Mathematics, Djillali Liabes University, Sidi Bel Abbès 22000, Algeria
Salih Djilali: Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées, Université de Tlemcen, Tlemcen, Algeria4Department of Mathematics, Faculty of Exact Sciences and Computer Science, Hassiba Benbouali University, Chlef 02000, Algeria
Anwar Zeb: Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Pakistan
Zareen A. Khan: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 08, 1-14

Abstract: We aim in this paper to study the effect of harvesting on predator–prey interaction in the case of prey herd behavior using a fractional-order model. Herd behavior has a crucial role in the surviving of species where it gave them the sufficient protection for the prey that perform it. The objective of using the fractional-order model is to model the memory effect measured by the order of the fractional derivative on the mutual interactions. Further, we aim to seek the effect of inner competition among the predators (also super-predators) on the evolution of the three species. For the mathematical results, we will show the local stability of the equilibria, and show the effect of memory rate and harvesting of the asymptotic behavior of the solution. Moreover, an efficient numerical scheme has been used to provide the numerical illustrations for our study.

Keywords: Food Chain; Predator–Prey Model; Fractional Derivative; Harvesting; Numerical Scheme (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402344

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