Dynamical Analysis in A Leslie-Gower Model Involving Allee Effect and Non-Linear Harvesting - Firdiansyah, Adin Lazuardy (KUBIK: Jurnal Publikasi Ilmiah Matematika, 2024)
The fishing industry has fished the Atlantic cod population for a millennium. As fishing became greater, the Atlantic cod population declined. During this crisis, fishing declined drastically, but the species is still struggling to bounce back. This is due to the growing number of sharks and other North Atlantic invertebrates. Based on this phenomenon, a Leslie-Gower model involving additive Allee effects and non-linear harvesting is considered to describe population dynamics. Further research is done on the existence and stability of equilibrium points as well as the positivity, permanence, and boundedness of solutions. It was found that the permanence requirement was used as a condition to ensure the two populations lived together. Numerical simulations are performed in the last section to bolster the analysis's findings.