Bifurcation Analysis in a Harvested Modified Leslie–Gower Model Incorporated with the Fear Factor and Prey Refuge

Fear and prey refuges are two significant topics in the ecological community because they closely associated with connectivity of natural resources. The effect fear on populations (proportional to both predator) is investigated nonlinear-type predator-harvested Leslie–Gower model. This type refuge much more sensible realistic than constant Because there less research dynamics this refuge, current study has been considered strengthen existing literature. number stability properties all positive equilibria examined. Since calculations for determinant trace Jacobian matrix quite complicated at these equilibria, certain evaluated using a numerical simulation process. Sotomayor’s theorem used derive precise mathematical confirmation appearance saddle-node bifurcation transcritical bifurcation. Furthermore, simulations provided visually demonstrate system limit cycle discussed help first Lyapunov number. We perform some sensitivity investigations our model solutions relation three key parameters: impact, refuges, harvesting. Our findings could facilitate biological understanding interactions between predators prey.