Dynamic Analysis of a Pest Management Smith Model with Impulsive State Feedback Control and Continuous Delay

Zhenzhen Shi, Yaning Li and Huidong Cheng
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Zhenzhen Shi: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Yaning Li: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Huidong Cheng: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Mathematics, 2019, vol. 7, issue 7, 1-15

Abstract: In our paper, we propose a single population Smith model with continuous delay and impulsive state feedback control. The application in pest management of this model is investigated. First, the singularity of this model is qualitatively analyzed; then, we consider the existence and uniqueness of order-one periodic orbit in order to determine the frequency of the implementation of chemical control. Moreover, based on the limit method of the sequences of subsequent points, we verify the stability of periodic orbit to ensure a certain robustness of this control; at last, we carry out the numerical simulations to verify the correctness of the theoretical results.

Keywords: unilateral diffusion; order-one periodic orbit; qualitatively analysis; Smith model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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