Optimization of an integrated feedback control for a pest management predator-prey model

In this paper, a Leslie-Gower predator-prey model with ratio-dependence and state pulse feedback control is established to investigate the effect of spraying chemical pesticides and supplement amount of beneficial insects at the same time. Firstly, the existence, uniqueness and asymptotic stability of the periodic solution are proved by using successor function method and the analogue of the Poincaré criterion when the equilibria E_∗ and E₀ are stable, and the existence of limit cycles without impulse system is verified when the equilibrium E_∗ is unstable. Furthermore, to obtain the minimum cost per period of controlling pests, we propose the optimization problem and calculate the optimal threshold. Finally, the feasibility of our model is proved by numerical simulation of a concrete example.