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

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.