Optimization of an integrated feedback control for a pest management predator-prey model
| Autor: | Yu Liu, Zhenzhen Shi, Yan Hui Wang, Hui Dong Cheng |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Food Chain
Insecta Optimization problem Population Dynamics Systems Theory 02 engineering and technology Feedback Exponential stability Control theory Successor function Limit cycle 0502 economics and business 0202 electrical engineering electronic engineering information engineering Animals Quantitative Biology::Populations and Evolution Computer Simulation Limit (mathematics) Uniqueness Pesticides Pest Control Biological Mathematics Computer simulation Applied Mathematics 05 social sciences General Medicine State (functional analysis) Models Theoretical Computational Mathematics Predatory Behavior Modeling and Simulation 020201 artificial intelligence & image processing Pest Control General Agricultural and Biological Sciences 050203 business & management |
| Zdroj: | Mathematical Biosciences and Engineering. 16:7963-7981 |
| ISSN: | 1551-0018 |
| DOI: | 10.3934/mbe.2019401 |
| Popis: | 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 Poincare 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. |
| Databáze: | OpenAIRE |
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