GEOMETRICAL ANALYSIS OF A PEST MANAGEMENT MODEL IN FOOD-LIMITED ENVIRONMENTS WITH NONLINEAR IMPULSIVE STATE FEEDBACK CONTROL

Tongqian Zhang; Tong Xu; Junling Wang; Yi Song; Zhichao Jiang

doi:10.11948/20190032

2019 Volume 9 Issue 6

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Tongqian Zhang, Tong Xu, Junling Wang, Yi Song, Zhichao Jiang. GEOMETRICAL ANALYSIS OF A PEST MANAGEMENT MODEL IN FOOD-LIMITED ENVIRONMENTS WITH NONLINEAR IMPULSIVE STATE FEEDBACK CONTROL[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2261-2277. doi: 10.11948/20190032

Citation:

Tongqian Zhang, Tong Xu, Junling Wang, Yi Song, Zhichao Jiang. GEOMETRICAL ANALYSIS OF A PEST MANAGEMENT MODEL IN FOOD-LIMITED ENVIRONMENTS WITH NONLINEAR IMPULSIVE STATE FEEDBACK CONTROL[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2261-2277. doi: 10.11948/20190032

GEOMETRICAL ANALYSIS OF A PEST MANAGEMENT MODEL IN FOOD-LIMITED ENVIRONMENTS WITH NONLINEAR IMPULSIVE STATE FEEDBACK CONTROL

1.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
2.
State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China
3.
Fundamental Science Department, North China Institute of Aerospace Engineering, Langfang 065000, China

Corresponding author: Email address:zhangtongqian@sdust.edu.cn (T. Zhang)
Fund Project: T. Zhang was supported by Shandong Provincial Natural Science Foundation of China (No. ZR2019MA003), SDUST Research Fund (No. 2014TDJH102) and Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents. T. Xu and J. Wang was supported by SDUST Innovation Fund for Graduate Students (No. SDKDYC190119). Z. Jiang was supported by National Natural Science Foundation of China (Nos. 11801014 and 11875001), Natural Science Foundation of Hebei Province (No. A2018409004), Hebei province university discipline top talent selection and training program (SLRC2019020) and Talent Training Project of Hebei Province

Abstract

Abstract

In this paper, a nonlinear impulsive state feedback control system is proposed to model an integrated pest management in food-limited environments. In the system, impulsive feedback control measures are implemented to control pests on the basis of the quantitative state of pests. Mathematically, an intuitive geometric analysis is used to indicate the existence of periodic solutions. The stability of periodic solutions is investigated by using Analogue of Poincaré Criterion. At last, numerical simulations are given to verify the theoretical analysis.
- Integrated Pest Management (IPM) /
- impulsive state feedback control /
- limited food environment /
- periodic solutions /
- stability
MSC: 34C25, 34C60, 92B05

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References

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