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

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 ord...

Full description

Saved in:
Bibliographic Details
Published inMathematics (Basel) Vol. 7; no. 7; p. 591
Main Authors Shi, Zhenzhen, Li, Yaning, Cheng, Huidong
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.07.2019
Subjects
Climate change
Control stability
Control systems
Ecosystems
Equilibrium
Feedback control
Food
Insects
Mathematical models
Mathematics
Orbital stability
Orbits
order-one periodic orbit
Pathogens
Population density
qualitatively analysis
Robust control
Smith model
State feedback
unilateral diffusion
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7070591