Modeling and Analyzing the Influence of Fear on the Harvested Modified Leslie-Gower Model

Abstract

A modified Leslie-Gower predator-prey model with a Beddington-DeAngelis functional response is proposed and studied. The purpose is to examine the effects of fear and quadratic fixed effort harvesting on the system's dynamic behavior. The model's qualitative properties, such as local equilibria stability, permanence, and global stability, are examined. The analysis of local bifurcation has been studied. It is discovered that the system experiences a saddle-node bifurcation at the survival equilibrium point whereas a transcritical bifurcation occurs at the boundary equilibrium point. Additionally established are the prerequisites for Hopf bifurcation existence. Finally, using MATLAB, a numerical investigation is conducted to verify the validity of the theoretical analysis and visualize the model dynamics.

Fear and Hunting Cooperation's Impact on the Eco-Epidemiological Model's Dynamics

“…However, the presence of a predator may drastically alter the prey's physiological and behavioral characteristics to the point where it may have a greater impact on the prey population than direct predation [17] and the mentioned references therein. There are many research studies using mathematical modeling considered the impact of hunting cooperation [1,[17][18][19][20][21][22][23][24][25] and the impact of fear [16,[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] in the prey-predator models separately. Numerous prey species alter their behavior when predators are around because of the possibility of being eaten.…”