Persistence and bifurcation analysis among four species interactions with the influence of competition, predation and harvesting

Shireen Rasool Jawad; Marwa Al Nuaimi

doi:10.24996/ijs.2023.64.3.30

Authors

Shireen Rasool Jawad Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0002-3090-8357
Marwa Al Nuaimi Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2023.64.3.30

Keywords:

Prey-predator model, Competition interaction, Harvesting, Stability, Local bifurcation

Abstract

In this paper, the interplay among four population species is offered. The system consists of two competitive prey, predator and super predators. The application of the hypothesis of the Sotomayor theorem for local bifurcation around every equilibrium point is adopted. It is detected that the transcritical bifurcation could occur near most of the system's equilibrium points, while saddle-node and pitchfork bifurcation can not be accrued at any of them. Further, the conditions that guarantee the accruing Hopf bifurcation are carried out. Finally, some numerical analysis is illustrated to confirm the analytical results.