Open AccessOptimization of an integrated feedback control for a pest management predator-prey model
Author(s) -
Zhen Zhen Shi,
Heng-Da Cheng,
Yu Liu,
Yan Hui Wang
Publication year - 2019
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2019401
Subject(s) - integrated pest management , predation , predator , pest control , biological pest control , feedback control , pest analysis , ecology , control theory (sociology) , natural enemies , environmental science , control (management) , biology , computer science , engineering , control engineering , artificial intelligence , botany
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 E 0 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.