### Mathematical Biosciences and Engineering

2019, Issue 6: 7963-7981. doi: 10.3934/mbe.2019401
Research article Special Issues

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

• Received: 04 March 2019 Accepted: 28 August 2019 Published: 02 September 2019
• 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 functions method and the analogue of the Poincaré criterion when the equilibria points $E_{*}$ and $E_{0}$ are stable, and the existence of the limit cycle without impulse system are verified when the equilibrium $E_{*}$ is the unstable point. 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.

Citation: Zhenzhen Shi, Huidong Cheng, Yu Liu, Yanhui Wang. Optimization of an integrated feedback control for a pest management predator-prey model[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 7963-7981. doi: 10.3934/mbe.2019401

### Related Papers:

• 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 functions method and the analogue of the Poincaré criterion when the equilibria points $E_{*}$ and $E_{0}$ are stable, and the existence of the limit cycle without impulse system are verified when the equilibrium $E_{*}$ is the unstable point. 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. ###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142 1.285 1.3

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