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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 4294595, 10 pages
Research Article

Qualitative Analysis of a Pest Management Gompertz Model with Interval State Feedback Impulsive Control

1School of Information Engineering, Dalian University, Dalian 116622, China
2School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China

Received 19 March 2016; Accepted 4 August 2016

Academic Editor: Manuel De la Sen

Copyright © 2016 Yuan Tian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An integrated pest management Gompertz model with interval impulsive control is put forward. Through pest density monitoring, an integrated control strategy is adopted; that is when pest density reaches an environmental damage level, pesticide is used as a control method; when pest density is lower than the damage level, predators as its natural enemy are released in case pest density is higher than the slightly harmful level and predator density is below its maintainable level. The analysis on the existence of order-1 or order-2 periodic orbit is carried out by the construction of Poincaré map of semicontinuous dynamical system. The stability and attractiveness of the periodic state are obtained by geometry approach, which ensures a certain robustness of control. The analytical results presented in the work are validated by numerical simulations for a specific model.