Effect of weak prey in Leslie–Gower predator–prey model

A Leslie–Gower prey–predator model incorporating partial prey protection is proposed. Prey densities are divided into two groups: strong and weak. The special dynamic of each group is considered. The condition of existence and uniqueness of the equilibrium point in the positive octant is determined, and by constructing a suitable Lyapunov function, it is shown that the unique equilibrium point is stable in the positive octant. The effects of strong prey becoming weak prey is studied and it is shown that it has no influence on the persistent property of the system and can enhance the co-existence of the prey–predator.