Dynamics of a Gilpin-Ayala predator-prey system with state feedback weighted harvest strategy

The current research presents a predator-prey model that incorporates both a Gilpin-Ayala growth function and a Holling type Ⅲ functional response. Two Lyapunov functions are established to confirm the global asymptotic stability of the positive equilibrium $P^{\ast }$ and the predator extinction equilibrium $P_k$. Considering ecological protection and commercial incentives, we also incorporated a weighted harvesting strategy and pulse control into the model. We investigated intricate dynamical problems instigated by the weighting harvesting and pulse effects, and affirmed the existence and local asymptotic stability of both predator-extinction periodic solution and positive order-1 periodic solution. In the end, a suite of numerical simulations were carried out using MATLAB, aiming to corroborate the theoretical findings and deliver conclusions rooted in a biological context.